







An analytic proof that a quadrilateral is a parallelogram 
20201026 

From Apollo: Prove analytically that if ABCD is a parallelogram in which points P and Q trisects the diagonal AC, then BPDQ is a parallelogram. Answered by Penny Nom. 





An exterior angle of a parallelogram 
20191129 

From A student: one angle of a parallelogram is four times the measure of the exterior angle adjacent to it. find the interior angles Answered by Penny Nom. 





Is a rectangle a parallelogram? 
20180228 

From ellie: is a rectangle a parallelogram? Answered by Penny Nom. 





A parallelogram, a rhombus and a rectangle 
20180207 

From Sambo: what do parallelogram, rhombus and rectangle have in common? Answered by Penny Nom. 





Parallel and Perpendicular lines 
20170717 

From Karen: Find an equation for the line with the given properties. Perpendicular to the line 7x + 2y = 6; containing the point (2, 1)
Find an equation for the line with the given properties. Parallel to the line 5x  3y =6; x intercept = 3 Answered by Penny Nom. 





Parallel lines 
20161026 

From Jordan: (7,5) 3x 4y=5 Answered by Penny Nom. 





A triple product 
20161003 

From sam: Let a and b are vectors such that
Vector a = (1,1,2)
Vector b = (2,1,1)
And let vector c be a unit vector such that triple product of a,b,c is
minimum . We have to find the value of c.
[Thoughts]
I thought triple product of a b, c means the volume occupied by
parallelepiped. And we have to do volume minimum Answered by Penny Nom. 





The sum of the angles of a triangle 
20160224 

From Sophia: Does every triangle add up to 180 degrees? (Such as a unique triangle) Answered by Penny Nom. 





The midpoints of the sides of a quadrilateral 
20160205 

From Andrea: The segments, joining, in order the midpoints of consecutive sides of a quadrilateral form a parallelogram. Answered by Penny Nom. 





Consecutive angles of a parallelogram 
20160128 

From Hanna: The consecutive angles of a parallelogram measures Answered by Penny Nom. 





Reinforced steel mesh in a circular foundation 
20150822 

From Padmesh: in a circular foundation we are laying a reinforced steel mesh . i.e., like chords in both ways. the circle diameter is 2.91m and rods are placed 0.1m spacing. so I want to find the number of rods present in that circle. here by I am attaching an auto cad drawing for your reference Answered by Penny Nom. 





Parallelogram area 
20150804 

From Nigel: To find the area of a parallelogram you multiply the base by the height of the parallogram, the height being determined by an imaginary line drawn at right angles to the base. However if I made a parallelogram with joints at each corner and maipulated it to an upright position where the base and sides were at 90 degrees to each other,, I could then simply multiply the base times the height to get the area. Since the sloping side of the parallelogram does not vary in my imaginary jointed model, why can I not simply multiply the base by the sloping side to get the area in the same way that I multiply the base times the height of a square to find its area ? I cannot find the answer to this on the internet although I have searched. Answered by Chris Fisher. 





Two parallel tangents to a circle 
20150305 

From Samantha: The equation of a circle is x^2+y^2=25. Determine
the equation of the parallel tangent lines to this
circle, for which the slope is 4/3. Answered by Penny Nom. 





A parallelogram inscribed in a circle 
20150204 

From narendra: how can we prove that a circular parallelogram is a rectangle? Answered by Chris Fisher. 





Interior angles in a parallelogram 
20140830 

From xavier: so, one of my math homework questions requires me to know how to find out how to find the interior angles in a parallelogram, the question is, "how many interior angles does a parallelogram have?" Answered by Penny Nom. 





Parallel chords 
20140306 

From Raj: AB andCD are two chords which are in the same side of the circle.The length of AB=12 and CD= 24.if the distance between them is 4 then find their radius. Pls help me I just believe on you guys I am having my exam after 3 days Answered by p. 





The area of a parallelogram 
20131128 

From shivam: a parallelogram has sides 34 cm and 20 cm .one of its diagonal is 42 cm. calculate its area Answered by Harley Weston. 





Euclid's Parallel Postulate 
20130820 

From Justin: Hello there,
I was wondering is Euclid's Fifth Parallel Postulate of parallel lines never intersecting, undecidable or essentially undecidable?
Thank you so much for any help you can provide! Answered by Robert Dawson. 





Two parallel chords of a circle 
20130730 

From Don: two parallel chords of a circle AB and CD on the same side from the center measure 6cm and 11 cm respectively. The distance between the 2 chords is 3 cm. Find the radius Answered by Penny Nom. 





A question about a parallelogram 
20121014 

From Renu: Question from renu, a parent:
ABCD is a parallelogram. BP and DQ are two parallel lines cutting AC at P and Q respectively. prove that BPDQ is a parallelogram Answered by Harley Weston. 





If a parallelogram is a cyclic quadrilateral then it is a rectangle 
20120201 

From Kim: Show that if a parallelogram is a cyclic quadrilateral then it is a rectangle.
Hint: Observe that in a parallelogram ABCD we always have Triangle ABC is congruent to Triangle CDA. Answered by Robert Dawson and Chris Fisher. 





Two parallel chords 
20111204 

From violet: Two parallel chords of a circle AB and CD on the same side of the centre measure 6 cm and 11 cm respectively. Find the radius. Answered by Chris Fisher and Walter Whiteley. 





The rate of change of the area of a parallelogram 
20110405 

From Gevork: Let a parallelogram have sides of 8 and 12 and let vertex angle A be decreasing at a rate of 2degrees per minute. Find the rate of change of the area of the parallelogram when angle A equals 30 degrees. Answered by Penny Nom. 





A transversal 
20110330 

From Jillian: I don't understand finding angels in a transversal Answered by Penny Nom. 





Slicing a rectangular parallelepiped 
20110223 

From tom: a) Pass a plane containing a vertex of a rectangular parallelepiped and a
diagonal of a face not containing that vertex to cut a pyramid from the
parallelepiped. What fraction of the volume of the parallelepiped is the
volume of the pyramid thus cut off?
b)Pass a plane through a cube of edge 8 in so that the section formed
will be a regular hexagon. Through each side of the hexagon pass two
planes, one plane containing one of the two vertices of the cube
which are farthest away from the plane of the hexagon, the other
plane containing the diagonally opposite vertex of the cube. Find the
volume of the solid bounded by these planes.
c)three of the edges of a rectangular parallelepiped that meet in a point
are also the lateral edges of a pyramid. What fraction of the parallelepiped
is this pyramid...?
you know the my only problem is how to illustrate this one...if only i
could ...can you help me....all I need is the drawing and I can do the rest
..it's fine if you'll only answer any of these but I'll be thankful if you
will do the three :).... Answered by Penny Nom. 





The diagonals of a parallelogram 
20110217 

From ginger: Find the diagonals of parallelogram where the the side is 40 and the bottom side is 15. Answered by Penny Nom. 





Area and volume of a parallelepiped 
20101214 

From ryan: Got a question, I'm really confused what the question mean and how the diagram would look like... someone please help... Here's the question.
The base of a parallelepiped is a rectangle 4m by 6m. If its lateral edge is 8m and is inclined at an angle 45 degrees to a 6m edge of the base, find the total area and volume of its parallelepiped.
My dilemma is what does it mean by the lateral edge of 8m is inclined at 45 degrees to a 6m edge of the base? Can someone post a diagram to help me solve the promble. Thanks in advance. Answered by Chris Fisher. 





Pyramids and parallelograms 
20100401 

From Vivi: Hi, my name is Vivi, and math teacher is giving a geometry test. I tend to forget how to find the surface area and volume of triangular pyramids and parallelograms. Do you have a way of remembering how to find the surface area? Answered by Harley Weston. 





A triangle problem 
20091028 

From Nazrul: ABC is a triangle , D is the mid point of AB and DE is parallel to BC where E lies on AC. How can I prove that E is the mid point of AC. Answered by Penny Nom. 





Forming a square 
20091021 

From christianah: Two parallel lines have the equations y=x+4 and y=x2.Two additional lines are drawn to form a square.What is the side length of the square?Write possible equations for the additional lines.Explain and justify your reasoning. Answered by Penny Nom. 





Parallel lines 
20090701 

From chris: Write the slope of a line that is parallel to each line.
1.y=2x5
2.y=x+2
3.3x+y=10
4.5xy=11
5.x+2y=6
6.2x3y=9
7.4x+y=3
8.x+2y=14 Answered by Brennan Yaremko. 





Parallel and perpendicular lines 
20090408 

From Blake: I need to know what the formula for working a problem. I need to know how to find if i line is parallel or perpendicular by only looking at the equation. i know you must know the slope but how do i find slope? Answered by Stephen La Rocque. 





The sides of a parallelogram 
20090317 

From Sami: If ABCD is a parallelogram, prove that line AB is congruent to line CD. Clearly state your reasons and conjectures. Answered by Penny Nom. 





The midpoints of two sides of a triangle 
20090317 

From Manis: Prove that the line joining the midpoint of two sides of a triangle is parallel to the third and half of it. Answered by Robert Dawson. 





A line parallel to a given line 
20090218 

From Lisa: I'm having a hard time understanding the concept of how to write an
equation of the line containing the given points and parallel to the given line.
Express the answer in the form of y=mx+b.
(7,9); 2x+5y=4. i would appreciate it alot if someone can show ne how
to do this. Thank you, Lisa Answered by Penny Nom. 





Are these lines parallel? 
20090206 

From Conor: are these lines parallel?
y = 3x 2 and 6y = 3x +2 Answered by Stephen La Rocque. 





The area of a triangle 
20090125 

From black: Explain how the formula for the area of a triangle can be determined by using the formula for the area of a parallelogram. Answered by Penny Nom. 





A quadrilateral with two pairs of congruent sides 
20081210 

From nicole: what is the name of a figure that has 2 sides that measure 25 feet each and 2 sides that measure 10 feet each? Answered by Robert Dawson. 





A quadrilateral with exactly 1 pair of parallel sides and no congruent sides 
20081210 

From alie: a quadrilateral with exactly 1 pair of parallel sides and no congruent sides is what? Answered by Robert Dawson. 





Symmetries of a parallelogram 
20081124 

From anisha: how many lines of symmetry does a parallelogram have. A square and a rect are a
parallelogram too. so it is confusing?? pls help Answered by Walter Whiteley. 





A geometric construction 
20081017 

From M: Given any 3 parallel lines on a plane, how to construct an equilateral triangle with each vertex on each line? Answered by Chris Fisher. 





How many parallel tangents may a circle have? 
20080929 

From Manish: how many parallel tangents may a circle have? the text book shows two.but a circle can have infinite tangents.then why not parallel tangents coz
theoretically each tangent have a parallel tangnts then no. of parallel tangent a circle may have is equals to half of the infinity i.e. infinity.. Answered by Walter Whiteley. 





Parallel Tangents 
20080924 

From manish: how many parallel tangents may a circle have? the text book shows two.but a crcle can have infinite tangents. Answered by Janice Cotcher. 





Parallel and perpendicular lines 
20080906 

From C: Can you help me determine whether these lines are parallel, perpendicular or neither and why?
Problem 1: y=3x+2
y=1/3x  4
Problem 2: y=1/3x + 1/2
y=1/3 x 2 Answered by Penny Nom. 





A line parallel to y= 1/2x + 5 
20080903 

From Michelle: Find the equation of a line parallel to y= 1/2x + 5 if the required line passes through ( 3,4) Answered by Penny Nom. 





A hexagon has 3 parallelograms 
20080721 

From Stephanie: A hexagon has 3 parallelograms but I am unsure of how to cut a hexagon into 3 parallelograms. Can you show me what this would look like? Answered by Harley Weston. 





The angles of a parallelogram 
20080611 

From light: ABCD is a parallelogram. If angle A. = (4x=17)degrees and angle B. = (3x5)degrees , what is angle c? Answered by Penny Nom. 





Naming a figure 
20080424 

From P.: What is the name of a figure that has 2 sides that measure
25 feet each and 2 sides that measure 10 feet each? Answered by Penny Nom. 





A parallel line to a given line 
20080412 

From john: A parallel line to a given line through a given point not on the a given line Answered by Harley Weston. 





The distance between the sides of a parallelogram 
20080330 

From jhon: Calculate the perpendicular distance between AB and DC of a parallelogram. Note: AB and DC are the sides of the parallelogram. Answered by Penny Nom. 





The interior angles of a parallelogram 
20080129 

From amber: the measure of one interior angle of a parallelogram is 42 degrees more than twice the measure of another angle. Find the measure of each angle. Answered by Penny Nom. 





The interior angles of a parallelogram 
20080128 

From steffie: How do you calculate the interior angle sof a parallelogram? Answered by Penny Nom. 





A parallelogram and a rhombus 
20080122 

From miguel: i have a problem proving a parallelogram a rhombus.. if a diagonal of a parallelogram bisects an angle
of the parallelogram , then its a rhombus
prove Answered by Stephen La Rocque and Walter Whiteley. 





A line parallel to a given line 
20071020 

From Samaira: Given Y=2/3 + 3/4x
Give the equation that is parallel to the given one and which touches the xaxis in x=3 Answered by Leeanne Boehm and Stephen La Rocque. 





Angle of depression to a football 
20070815 

From Tosin: The angle of depression to a football from the top of building 10m high
is 17 degrees. Find the distance of the ball from the foot of the building. Answered by Stephen La Rocque. 





Proving a quadrilateral is a rectangle 
20070714 

From Sonja: I was having this discussion with another teacher and we need a third opinion. When you are trying to prove a quadrilateral is a rectangle which method should you use:
 Prove the shape is a parallelogram by doing slope 4 times by stating that parallel lines have equal slopes. Then proving a right angle by stating that perpendicular lines have negative reciprocal slopes.
 Doing the slope 4 times and stating that the shape is a rectangle because opposite sides are parallel because of equal slopes and it contains a right angle because of negative reciprocal slopes.
I guess the real question is do you have to first state that the shape is a parallelogram? Answered by Stephen La Rocque. 





The law of sines 
20070609 

From Felicia: A parallelogram has one side that is 12.0 cm and one angle that is 65°. The shorter diagonal is 25.0 cm. To the nearest tenth of a centimetre, how long is the other side of the parallelogram? Use the sine law. Answered by Penny Nom. 





The distance between parallel lines 
20070528 

From Kristie: I can't figure out how to determine the distance between parallel lines I am taking
linear algebra and vector geometry. I was given two lines in the form #x+#y =#
told they were parallel and asked to find the distance between them??
Please help
Thanks Answered by Penny Nom. 





Slicing a doublenapped cone with a plane 
20070507 

From Andrew: I am writing a paper about creating parallel lines by slicing a doublenapped cone with a plane. I have found out how it can be shown by algebra that the equations for parallel lines are generated from the degenerate case of a second degree polynomial in two variables, but I have yet to find a source with a visual representation of this case. Do you know if it exists? Answered by Chris Fisher. 





Finding out if two line equations are parallel or perpendicular 
20070428 

From Vincent: Can you determine if the two lines are parallel, perpendicular, or neither
1/2x+4y=3/5
y/1 + 10/5= 8x
I think there perpendicular but how would you solve the equations Answered by Stephen La Rocque. 





Two parallel lines 
20070425 

From prasanna: Let me know the Equation of a line which is parallel to some other line at a distance of Dmts. Answered by Penny Nom. 





A line that is perpendicular to another line 
20070316 

From Jesse: How do you write an equation of a line that is perpendicular to
y+2x+3 and passes through (3,4); I don't understand the steps
of how to do this???? Answered by Stephen La Rocque and Penny Nom. 





Prove that the triangle ABC is isosceles 
20070305 

From Lisa: I am stuck on this problem... If AB = CD (parellel line), and Answered by Stephen La Rocque and Penny Nom. 





Parallel lines 
20070227 

From Jennifer: How to you decide whether the graphs of these two equations are parallel linse: y=3x+2, y=1/3x+4 Answered by Stephen La Rocque and Penny Nom. 





The interior angles of a parallelogram 
20070207 

From jenniffeir: Can a parallelogram have two 45 degree angles and two 75 degree angles? Answered by Haley Ess. 





The diagonals of a parallelogram are mutually bisecting 
20070121 

From Greta: I am having trouble proving that the diagonals of a parallelogram are mutually bisecting. Answered by Penny Nom. 





Two consecutive angles of a parallelogram 
20070117 

From Veronica: The measures of two consecutive angles of a parallelogram are in the ratio 9:11. Find the measure of each angle. Answered by Penny Nom. 





A line through the point (4, 7) and parallel to the line y=2 
20070114 

From Chasity: i am suppose to write an equation of a line through the point (4, 7) and parallel to the line y=2. please help me Answered by Penny Nom. 





Parallel and perpendicular lines 
20061207 

From Valeria: I m having trouble with parallel and perpendicular lines a problem i need help with is y=6 find the slope if al line parallel to the graph of each equation Answered by Stephen La Rocque. 





Family of lines 
20060929 

From Sasha: could a "Family of Lines" have both parallel and intersecting equations that aren't related directly but otherwise related by each other to create a curve Answered by Chris Fisher. 





An angle in a parallelogram 
20060813 

From Sam: Parallelogram ABCD has diagonal AC equal in length to side AB. CD is produced to E so that D is between E and C. If angle BAC =30 degrees find the size of angle ADE. Answered by Stephen La Rocque. 





A line parallel to a plane 
20060328 

From Ryan:
I was wondering how I would prove the following theorem. I am completely lost at this point and all my other ideas have been extremely complicated and somewhat blurry.
"Through a point outside a given plane, there is at least one line parallel to the given plane."
Answered by Chris Fisher. 





The area of a parallelogram 
20060312 

From Shayne: Is there a method of finding the area of a trapezium or/and parallelogram even if the height is not given? Could you also explain how to find the height? Answered by Penny Nom. 





Two parallel lines 
20060122 

From Marbara: On my math homework I have a problem where it says find the value of x so that L is parallel to M
on one of the there are three lines. the top one is horizontal which is L. the bottom one is also horizontal directly under L which is M. there is another line that is diagonal going through the middle sections of L and M.
To the right of the diagonal line and right under line L is an equation 5x10
to the right of the diagonal line and right above line M is an equation 8X5
I tried to find what X is but I can't because it never matches both equations no matter what way I try to do it. Answered by Penny Nom. 





What is the angle between 2 noncollinear parallel lines? 
20051017 

From Ben: What is the angle (if any) between 2 noncollinear parallel lines? Answered by Chris Fisher and Walter Whiteley. 





A theorem involving a trapezoid 
20040929 

From Abraham: Given:Trapezoid ROSE with diagonals RS and EO intersecting at point M
Prove:Diagonals RS and EO do not bisect each other. Answered by Harley Weston. 





A parallelepiped 
20040925 

From Aman: " If OA, OB, and OC are three edges of a parallelepiped where O is (0,0,0), A is (2,4,2), B is (3,6,1), and C is (4,0,1), find the coordinates of the other vertices of the parallelepiped.)" Answered by Penny Nom. 





A parallelogram 
20040730 

From Keith: I'm a high school student and have been having trouble with this problem , which is based on one pair of parallel sides of a parallelogram: If AD = 6x5 and BC = 3x+7 find x. Of course both sides have to be equal. Now I know the value of x is 4 So my question is how do you get 4 from the given information. Answered by Penny Nom. 





What is the name of a 3D rectangle? 
20040607 

From Jack: if a cube is a 3D square, what is the name of a 3D rectangle? Answered by Penny Nom. 





Can 2 vertical planes intersect? 
20030906 

From Erin: My question is can 2 vertical planes intersect? Answered by Penny Nom. 





The area of a parallelogram 
20030406 

From A student: Find the area of the parallelogram with vertices (0,0),(7,2),(10,7),(3,5) Answered by Penny Nom. 





Can a square be a rhombus? 
20030304 

From Beth: Can a square be a rhombus? Some sources say yes, some say no. Some sources define a rhombus as a quadrilateral and parallelogram with equal sides, but without right angles. Some sources say a square is a special case of a rhombus. Clarity, please! Answered by Walter Whiteley. 





Can a square be considered a rectangle? 
20030227 

From Carla:
Can a square be considered a rectangle? (since opposite sides are same length and parallel) Would a regular hexagon or octagon be considered a parallelogram since its opposite sides are parallel? or does a parallelogram HAVE to have only 4 sides? Answered by Penny Nom. 





Parallelograms 
20020821 

From Moorthy: 11 parallel lines are intersected by another 9 parallel lines.Then how many parallelograms are formed? Answered by Walter Whiteley. 





How can you prove a quadrilateral to be a parallelogram? 
20010316 

From Joy: How can you prove a quadrilateral to be a parallelogram? Answered by Walter Whiteley. 





Kinds of lines 
20010209 

From Robyn: What are the different kinds/types of lines? Answered by Leeanne Boehm. 





Parallel tangents 
20000630 

From Ebony Indalecio: I need to prove the theroem: Tangents to a circle at the end points of a diameter are parallel. Answered by Walter Whiteley. 





Parallel and perpendicular lines 
20000508 

From Jimmy Lumpkins: Need a method for solving the following problem: Find the equation of a line through point P that is parallel or perpendicular to another line. Answered by Paul Betts. 





Congruent parts of congruent figures 
20000310 

From Erica: Yesterday, I recieved a test problem asking to prove two line segments equal. Here is the problem as I was given it: Given: paralleogram ABCD AE is perpendicular to DB CF is perpendicular to DB Prove: AE is equal to CF I answered the problem as follows: . . . Answered by Walter Whiteley. 





Parallel lines 
20000112 

From Lori: Find an equation of the line parallel to the given line containing the given point. x + y = 2; (1,2) We know parallel line have the same slope and we know the answer y = x + 3. Answered by Penny Nom. 





Three dimensional rectangle 
20000111 

From Dennis Murphy: I would like to find out the name of a Three dimensional rectangle. Answered by Harley Weston. 





Parallel planes 
20000110 

From Hugo Alvarez: When two parallel planes are cut by a third plane, the lines of the intersection are? Answered by Claude Tardif. 





Parallel and perpendicular lines 
19990423 

From Crystal Pilling: My name is Crystal Pilling and I am in 9th grade algebra. We are currently studying parallel and perpendicular lines. I am having trouble with this problem: 3/4x  5y= 16, (5,6) I have to find a line that is perpindicular to this line on a graph. HELP ME PLEASE!!!!! Answered by Penny Nom. 





Universal Area 
19990408 

From Karen Richardson: I need a formula for area that works for a square, a rectangle, a parallelogram, a trapezoid, and a triangle. Answered by Jack LeSage, Chris Fisher and Harley Weston. 





Circumference and Area 
19990216 

From Natalie: finding the circumference of a circle? formula finding the area of a parallelogram? formula
Answered by Penny Nom. 





A Horizontal Line 
19980923 

From Tess Warer: Find the equations of a line through (1,5) and parallel to the Xaxis. Answered by Harley Weston. 





Isosceles trapezoid formula 
19980512 

From Donna McMullin: The teacher of Gifted and Talented Math has been trying to locate the formula for anisosceles trapezoid and we can't find it anywhere. Could it be the same formula for that of a parallelogram ? Please advise. Answered by Walter Whiteley. 





Intersecting Lines. 
19980210 

From Erik Heppler: My typewriter frequently makes mistakes. Suppose I gave you the following system of equations to solve: 35.26X + 14.95Y = 28.35 187.3X + 79.43Y = 83.29 When I looked back, I realized that I meant to use 14.96 as the "Y" coefficient in the first equation instead of 14.95. Solving the system using 14.95 and then solving another system using 14.96 with all other values the same both times results in the intersection points (1776, 4186) and (770, 1816) respectively. How can that be? Answered by Penny nom. 





Shimin's Geometry Problem 
19971202 

From Ong Shimin: ABCD is a rectangle. X and Y are the midpoints of BC and CD respectively. W is a point on AB such that AW : WB = 2 : 1. Z is a point on AD such that AZ : ZD = 2 : 1. WY intersects XZ at O. If the area of triangle WOZ is 84 centimeters squared, find the area of triangle XOY. Answered by Chris Fisher. 





Prove that these two lines are parallel. 
19960529 

From Adam Piekarzewski: Using parallel line theorems and side angle side etc. in triangle acd a line is drawn from point b on ac and point i on ad. another triangle fliped vertically and joined at d is named fdh, a line is drawn from point e on fd and point g on fh. ab = fg, ai = fe, ac  fh prove that bi  eg / / Answered by Harley Weston. 

