Question

1. write the conclusion for the statement. if m∠qrs + m∠lmn = 223° and 223° = m∠ghi, then...

complete the table with the reason that makes the given statement true.

statement	reason
9. ∠mnp≅∠dfg	congruent angles have equal measure by definition

1. triangles abc and def are shown.

fill in the blanks using the information shown on the two triangles.
ef = ____. therefore, ef≅ ____.
m∠cab = ____. therefore, ∠cab≅ ____.
are triangles abc and def congruent? explain.

Explanation:

Step1: Identify side lengths

From the figure, $EF = 4$ and $AB = 4$, so $\overline{EF}\cong\overline{AB}$.

Step2: Identify angle measures

$m\angle CAB = 96^{\circ}$ and $m\angle FED=96^{\circ}$, so $\angle CAB\cong\angle FED$.

Step3: Check congruence

Inspect the triangles for congruence criteria. Criteria are not met.

Answer:

EF = 4. Therefore, $\overline{EF}\cong\overline{AB}$.
$m\angle CAB = 96^{\circ}$. Therefore, $\angle CAB\cong\angle FED$.
No, the triangles are not congruent. While $\angle CAB\cong\angle FED$ and $\overline{EF}\cong\overline{AB}$, the side - angle - side (SAS), angle - side - angle (ASA), angle - angle - side (AAS), and side - side - side (SSS) congruence criteria are not met.