Chapter 4.6, Problem 14WE

To determine

To prove: $\angle ABC\cong \angle ACB$ .

Explanation of Solution

Given Information:

Given figure,

  

  $\overline{AB}\cong \overline{AC}$ ;

  $\overline{AB}$ and $\overline{AC}$ are extended so $\overline{BD}\cong \overline{CE}$ .

Key steps of proof:

a. $\Delta DAC\cong \Delta EAB$

b. $\Delta DBC\cong \Delta ECB$

c. $\angle DBC\cong \angle ECB$

d. $\angle ABC\cong \angle ACB$

Calculation:

Consider the following data.

  $\overline{AB}\cong \overline{AC}$

Lines $\overline{AB}$ and $\overline{AC}$ are extended so $\overline{BD}\cong \overline{CE}$ .

Following the key steps of the proof given in the book, write the proof in paragraph form:

By the Side angle postulate $\Delta DAC\cong \Delta EAB$

By the Side-Side-Side postulate $\Delta DBC\cong \Delta ECB,\angle DBC\cong \angle ECB$ as these are the corresponding parts of congruent triangles.

  $\angle ABE\cong \angle ACD,\angle CBE\cong \angle BCD$ .

Therefore, $\angle ABC\cong \angle ACB$ as one angle is part of the other.

Hence, it is proved that $\angle ABC\cong \angle ACB$ .