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Part A

The two figures, ΔABC and ΔPQR are congruent by the SSS rule of congruency

Part B

The rigid motion that maps ΔABC to ΔPQR are a 180° clockwise rotation about the origin, followed by a horizontal shift of 1 unit to the right

Step-by-step explanation:

Part A

The given coordinates of the vertices of triangle ABC are;

A(-8, -2), B(-3, -6), C(-2, -2)

The length of side AB = √((-6 - (-2))² + (-3 - (-8))²) = √41

The length of side AC = √((-2 - (-2))² + (-2 - (-8))²) = 6

The length of side BC = √((-6 - (-2))² + (-3 - (-2))²) = √17

The given coordinates of the vertices of triangle PQR are;

P(9, 2), Q(4, 6), R(3, 2)

The length of side PQ = √((6 - 2)² + (4 - 9)²) = √41

The length of side PR = √((2 - 2)² + (3 - 9)²) = 6

The length of side RQ = √((6 - 2)² + (4 - 3)²) = √17

Given that the length of the three sides of triangle ABC are equal to the lengths of the three sides of triangle PQR, we have;

ΔABC ≅ ΔPQR by Side Side Side rule of congruency

Part B

Whereby AB and PQ, and BC and RQ are pair of corresponding sides, the rigid motion that maps ΔABC to ΔPQR are;

1) A 180° clockwise (or counterclockwise) rotation about the origin followed by

2) A shift of 1 unit to the right.