Question

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

1. m∠mnp = m∠dfg
2. ∠mnp ≅ ∠dfg
3. 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 ≅ ∠fed.
are triangles abc and def congruent? explain.

Explanation:

Step1: Identify side lengths

From the figure, EF = 4 and AB = 4, so EF ≅ AB.

Step2: Identify angle measures

∠CAB = 90° and ∠FED = 90°, so ∠CAB ≅ ∠FED.

Step3: Check congruence

We only have two pairs of congruent parts, not enough for congruence postulates.

Answer:

EF = 4. Therefore, EF ≅ AB.
m∠CAB = 90°. Therefore, ∠CAB ≅ ∠FED.
No, the triangles are not congruent. While two pairs of corresponding parts are congruent, we don't have enough information (like side - angle - side (SAS), angle - side - angle (ASA), etc.) to prove congruence.