Question

given: ∠teg≅∠had
prove: m∠fet + m∠had = 180°
complete the proof below.
statements

1. m∠fet + m∠teg = 180°
2. ∠teg≅∠had
3. choose your answer_
4. m∠fet + m∠had = 180°

reasons

1. choose your answer_
2. choose your answer_
3. segment addition postulate, definition of complementary, definition of supplementary (linear pair), angle addition postulate

Explanation:

Step1: Identify linear - pair property

$\angle FET$ and $\angle TEG$ form a linear pair. By the definition of supplementary (linear pair), the sum of the measures of two angles in a linear pair is $180^{\circ}$, so $m\angle FET + m\angle TEG=180^{\circ}$.

Step2: Use given information

The given statement is $\angle TEG\cong\angle HAD$. This is given in the problem.

Step3: Substitute equal - angle measures

Since $\angle TEG\cong\angle HAD$, then $m\angle TEG = m\angle HAD$. Substituting $m\angle TEG$ with $m\angle HAD$ in the equation $m\angle FET + m\angle TEG = 180^{\circ}$, we get $m\angle FET + m\angle HAD=180^{\circ}$.

Answer:

1. Definition of supplementary (linear pair)
2. Given
3. $m\angle TEG = m\angle HAD$; Substitution Property of Equality
4. Substitution (from step 1 and 3)