Question

C is the circumcenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent?

It is given that triangle ABD is an isosceles triangle, so segments AB and DB are congruent by the definition of isosceles triangle.
It is given that C is the circumcenter of triangle ABD, making segment BE a perpendicular bisector.
By the definition of perpendicular, angles AEB and DEB are 90°, so triangles ABE and DEB are right triangles.
Triangles ABE and DEB share side AD making it congruent to itself by the reflexive property.
Triangles ABE and DBE are congruent by HL.

A. There is an error in line 1; segments AB and BD are given to be congruent.
2. There is an error in line 4; segment AD is not a shared side.
3. There is an error in line 3; segment BE should be a median.
D. The proof is correct.

Not D

Answer 1

@Jasminexx

Answer 2

@dude

Answer 3

@mhchen

Answer 4

- Pay attention to wording
AED is part of the whole triangle, not each AEB and DEB

Answer 5

ok