SOLUTION: can you help me with this please...Thank you Given:ABCD is a rectangle E is the midpoint of line AD Prove: traingle BEC is isosceles please help... really appre

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Question 174240: can you help me with this please...Thank you
Given:ABCD is a rectangle E is the midpoint of line AD
Prove: traingle BEC is isosceles

please help... really appreciate it thank you
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
Draw the rectangle ABCD. Then add in point E. E is the midpoint of AD. So the length AE = ED.
Now draw in line segments BE and CE.
What you have now are a rectangle that is composed of 3 smaller triangles. The triangles are ABE, BEC and DEC.
You are asked to prove BEC is isosceles. That means you must prove BEC has two sides of equal length.
Look at triangles AEB and DEC. You know a rectangle has 4 90 degree angles in it. So the angles EAB and EDC are both 90.
You know the tow lengths AE and ED are equal.
You also know that opposite sides of a rectangle are eqaul in length. So AB = CD.
Side-angle-side is one way to prove two triangles are congruent. ABE and DEC have SAS congruence. Congruent triangles have all 3 sides equal. So BE = EC.
Thus BEC has two equal sides and must be, therefore, be isosceles