Question

2 δpqr: p(-7, -1), q(4, 9), r(-2, -5), δxyz: x(-11, 4), y(0, -6), z(-1, 3)
pq = √(4+7)² + (9+1)² = √221\txy = √(0+11)² + (-6-4)² = √221
qr = √(4+2)² + (9+5)² = √232\tyz = √(0+1)² + (-6-3)² = √81
pr = √(-7+2)² + (-1+5)² = √41\txz = √(-11+1)² + (4-3)² = √101
are the triangles congruent? if yes, explain your reasoning and write a congruency statement.
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Explanation:

Step1: Recall Congruence Condition

Two triangles are congruent if all corresponding sides are equal (SSS congruence). We check the lengths of all sides of \( \triangle PQR \) and \( \triangle XYZ \).

Step2: Analyze Side Lengths

• \( PQ = \sqrt{221} \), \( XY = \sqrt{221} \) (one pair equal).
• \( QR = \sqrt{232} \), \( YZ = \sqrt{81}=9 \) (not equal, \( \sqrt{232}\approx15.23

eq 9 \)).

• \( PR = \sqrt{41}\approx6.40 \), \( XZ = \sqrt{101}\approx10.05 \) (not equal).

Since not all corresponding sides are equal, the triangles do not satisfy SSS congruence.

Answer:

No, the triangles are not congruent. Because the lengths of corresponding sides (\( QR \) & \( YZ \), \( PR \) & \( XZ \)) are not equal, so SSS congruence condition is not met.