Question

1. which parts must be congruent to prove that δmud ≅ δcat by the asa postulate? a. $overline{mu}congoverline{ca}$ b. $overline{md}congoverline{ct}$ c. $overline{ud}congoverline{at}$ d. $angle mcongangle c$ 11. which postulate or theorem can be used to prove that δtlc ≅ δbkw? a. asa b. ssa c. sas d. the triangles cannot be proved to be congruent.

Explanation:

Step1: Recall ASA postulate

The ASA (Angle - Side - Angle) postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step2: Analyze question 10

For $\triangle MUD$ and $\triangle CAT$ to be congruent by ASA, we need two pairs of angles and the included side to be congruent. Looking at the options, we need the pair of angles and the side between them. The correct pair of angles is $\angle M\cong\angle C$ (along with the appropriate included - side pair which is not among the options here). So for question 10, the answer is D.

Step3: Recall triangle - congruence postulates and theorems

The SSA (Side - Side - Angle) is not a valid postulate for proving triangle congruence in general. The ASA (Angle - Side - Angle) requires two angles and the included side, and the SAS (Side - Angle - Side) requires two sides and the included angle.

Step4: Analyze question 11

If we assume from the figure (not shown here in detail but based on the options) that we have two sides and the included angle congruent between $\triangle TLC$ and $\triangle BKW$, we use the SAS postulate. So for question 11, the answer is C.

Answer:

1. D. $\angle M\cong\angle C$
2. C. SAS