BRM = KYZ how can you justify that YZ = RM
A. CPCTC
B. SAS
C. ASA
D. SSS
C. ASA (Angle-Side-Angle)
which statement cannot be justified given that PBJ=TIM
A. PB=TI
B. B=I
C. BJP=IMT
D. JP=MI
B. B = I
To justify that YZ = RM, we can use the CPCTC (Corresponding Parts of Congruent Triangles are Congruent) theorem. This theorem states that if two triangles are congruent, then their corresponding sides and angles are also congruent.
Since BRM = KYZ, this means that triangle BRM is congruent to triangle KYZ. Therefore, corresponding sides of these triangles are congruent, which includes YZ = RM.
So, the correct answer is A. CPCTC.
To justify that YZ = RM, we need to determine which geometric theorem or postulate can be applied to prove the congruence of two line segments. Let's explore the options:
A. CPCTC (Corresponding Parts of Congruent Triangles are Congruent): This theorem states that if two triangles are congruent, then their corresponding parts are congruent. However, the given information does not mention anything about triangles, so CPCTC is not applicable in this case.
B. SAS (Side-Angle-Side): This theorem states that if two triangles have two pairs of sides congruent and the included angle congruent, then the triangles are congruent. Again, the given information does not mention anything about triangles, so SAS is not applicable.
C. ASA (Angle-Side-Angle): This theorem states that if two triangles have two pairs of corresponding angles congruent and the included side congruent, then the triangles are congruent. However, we are not given any angles, so ASA is not applicable.
D. SSS (Side-Side-Side): This theorem states that if three pairs of corresponding sides of two triangles are congruent, then the triangles are congruent. Since BRM = KYZ, we have two pairs of corresponding sides that are congruent. Hence, we can apply the SSS theorem to justify that YZ = RM. Thus, the correct answer is (D) SSS.