Math CentralQuandaries & Queries


Question from alex, a student:

if a convex quadrilateral ABCD is set up so that angles b and c are fixed (for example angle b= 73 and angle c =150), and sides AB and CD are congruent; can angles a and b vary, or are they also fixed

Dear Alex,
What a great question!
Your best bet is to not get tied down by the wordiness of the problem. Try drawing a diagram. I'm assumming that angles b and c would be next to each other, that'll help in your drawing. Also, AB and CD have to be the same length. Try invisioning yourself moving the drawing around. Do things like making a side longer and changing an angle. Just remember:
1) you can't change angles b or c
2) AB and CD are the same length. So you can change their length, but what you do to one you must do to the other.

You will find one of two things. Either you'll be able to move the quadrillateral around a lot and change the other angles, meaning that the other angles or not fixed. OR, you can't move it that much and the angles will stay the same.

Hope these tips help!


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