Question

Given ABCD is a parallelogram, identify which theorem (ASA, SAS, or SSS) to prove two triangles congruent. Then make a conclusion that segment AM is congruent to segment CM.

Answer 1

The SAS (Side-Angle-Side) congruence theorem is used to prove the congruence of two triangles in a parallelogram. To prove that segment AM is congruent to segment CM, we can show that triangle AMC is congruent to triangle MCB by proving congruent sides and congruent angles.

Step-by-step explanation:

The theorem to prove the congruence of two triangles in a parallelogram is SAS (Side-Angle-Side) congruence theorem.

To prove that segment AM is congruent to segment CM, we can use the SAS congruence theorem by showing that triangle AMC is congruent to triangle MCB.

We can prove this by:

1. Showing that segment AM is congruent to segment CM (given).
2. Showing that segment AC is congruent to segment CB (opposite sides of a parallelogram are congruent).
3. Showing that the included angle angle AMC is congruent to the included angle angle MCB (opposite sides of a parallelogram are parallel, so angles AMC and MCB are corresponding angles and thus congruent).

By proving these three conditions, we can conclude that segment AM is congruent to segment CM in the parallelogram ABCD.