Question

Geometry Question - Given: segment AD = segment BC, angle DAB = angle CBA; Prove: triangle ABE is isosceles (reference diagram and problem in picture)

Answer 1

ABC is an isosceles triangle with BA = BC. D lies on AC. ABD is an isosceles triangle with AB = AD. Angle ABD = 72° Show that the triangle BCD is isosceles.
11 pages·10 MB

Answer 2

sidesAs given by the question

There are given that ;

`\begin{gathered} AD=BC \\ \angle DAB\cong\angle CBA \end{gathered}`

Now,

From the properties of an isosceles triangle, we also know that in an isosceles triangle, the altitude from the apex angle that bisects the base and the apex angle

So,

According to the question and also properties of an isosceles triangle

There are two equal side and the two angles opposite to the equal sides are equal and one line of symmetry.

So, we can say that triangle ABE is isosceles.

Hence, proved.