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Congruent right triangles: find a missing side by correspondence and Pythagoras

This type of question, asked 2 times: 14 Jul 2023 S2, 24 Sep 2024 S2. All 2 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S2

    68
    Let ABC, PQR be two congruent triangles such that angle A = angle P = 90∘90^\circ. If BC = 13cm, PR = 5cm, find AB.

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  2. Question 2

    24 Sep 2024 S2

    62
    In ΔDEF\Delta DEF, DE = 12 cm, EF = 15 cm, and ∠DEF=90∘\angle DEF = 90^\circ. ΔDEF\Delta DEF is congruent to ΔXYZ\Delta XYZ. If YZ = 15 cm, then what is the length of XZ?

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