Question

in the proof of △abc≅△def, which statement correctly uses cpctc? a. ∠a = ∠d because they are corresponding parts of congruent triangles. b. bc≠de, since congruent triangles are only partially congruent. c. ab = ef because both triangles are isosceles. d. ∠b = ∠e because their vertices match. if triangles mno and pqr are congruent by sss with mn = 8 cm, no = 10 cm, and mo = 12 cm, what is the length of pq? a. 10 cm b. 12 cm c. 14 cm d. 8 cm what is the first step in using cpctc in a proof? a. draw the triangles b. prove the triangles are congruent c. measure the angles d. identify corresponding parts

Explanation:

Step1: Recall CPCTC concept

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent". It can only be used when two triangles are proven to be congruent.

Step2: Analyze first question

For the statement "In the proof of $\triangle ABC\cong\triangle DEF$, which statement correctly uses CPCTC?", option a. $\angle A=\angle D$ because they are corresponding parts of congruent triangles is correct as it applies the CPCTC principle. Option b is wrong as congruent triangles are fully congruent. Option c is wrong as it gives an incorrect reason related to isosceles - triangles instead of CPCTC. Option d is wrong as just vertex - matching is not a valid CPCTC application.

Step3: Analyze second question

If $\triangle MNO$ and $\triangle PQR$ are congruent by SSS (Side - Side - Side) and $MN = 8$ cm, $NO=10$ cm, $MO = 12$ cm. By CPCTC, corresponding sides are equal. If $MN$ corresponds to $PQ$ (by the order of congruence), then $PQ=MN = 8$ cm. So the answer is d.

Step4: Analyze third question

The first step in using CPCTC in a proof is to prove that the triangles are congruent. Without proving the triangles are congruent, we cannot use CPCTC. So for "What is the first step in using CPCTC in a proof?", the answer is b.

Answer:

1. a. $\angle A=\angle D$ because they are corresponding parts of congruent triangles.
2. d. $8$ cm
3. b. Prove the triangles are congruent.