Question

If ALMN = AXYZ, which congruences are true by CPCTC? Check all that apply:

A. ML = XZ
B. IN = YX
C. ME = ZE
D. LZ = EN
E. ZY = ZN

Answer 1

CPCTC is a theorem in geometry that states if two triangles are congruent, then their corresponding parts are congruent. By applying CPCTC in the given situation, we can determine which congruences are true.

Step-by-step explanation:

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent. It is a theorem in geometry that states if two triangles are congruent, then their corresponding parts, such as sides and angles, are also congruent. In this case, if ALMN = AXYZ, we can conclude that the corresponding parts of the triangles are congruent by CPCTC.

A. ML = XZ: Yes, this is true because M and X are corresponding points of the triangles ALMN and AXYZ, and L and Z are corresponding points.

(B) IN = YX: No, this is not true. There is no corresponding pair of sides that includes I and Y.

C. ME = ZE: No, this is not true. There is no corresponding pair of sides that includes M and E.

(D) LZ = EN: Yes, this is true. L and E are corresponding points, and Z and N are corresponding points.

(E) ZY = ZN: Yes, this is true. Z and Z are corresponding points, and Y and N are corresponding points.