Chapter 6.1, Problem 18PSC

To determine

To show that triangle AXD is an isosceles triangle.

Answer to Problem 18PSC

  $\Delta AXD isanisosceles triangle.$

Explanation of Solution

Given information:

  $\Delta ABC \cong \Delta DBC$

Formula used:

The below properties are used:

Two triangles are congruent by SAS congruence rule.

If two sides of a triangle are congruent, the triangle is isosceles.

Proof:

It is given that,

  $\Delta ABC \cong \Delta DBC$

  

As corresponding parts of congruent triangles are congruent, we get

  $\angle ABC\cong \angle DBC$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{AB} \cong \overline{DB}$

By reflexive property, we get

  $\overline{BX} \cong \overline{BX}$

By SAS congruence rule, we get

  $\Delta ABX \cong \Delta DBX$

As corresponding parts of congruent triangles are congruent, we get

  $\overline{AX} \cong \overline{DX}$

If two sides of a triangle are congruent, the triangle is isosceles.

  $\Delta AXD isanisoscelestriangle .$