







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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 





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 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 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. 





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. 





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 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. 





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. 





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. 





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. 





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. 





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. 





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. 





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. 

