Chapter 4.4, Problem 30WE

To determine

To Find: A pair of congruent triangles.

Answer to Problem 30WE

  $\Delta ACD\cong \Delta ABD$

Explanation of Solution

Given information:

In the figure shown, $\Delta ABC\text{in plane}M$ , $D\text{not}\text{in plane}M$ , $\angle ACB=\angle ABC$ and $\angle DCB=\angle DBC$ .

  

Calculation:

Using two-column proof.

Statements	Reasons
$\angle ACB=\angle ABC$	Given
$AC=AB$	If in a triangle, base angles are congruent, the sides opposite to these angles are also congruent
$\angle DCB=\angle DBC$	Given
$DC=DB$	If in a triangle, base angles are congruent, the sides opposite to these angles are also congruent
$AD=AD$	Reflexive property
$\Delta ACD\cong \Delta ABD$	By SSS Postulate

Therefore, $\Delta ACD$ and $\Delta ABD$ are congruent.