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One angle and one adjacent side equal: which further equality makes the triangles congruent by SAS

The same question, asked 2 times: 14 Jul 2023 S1, 12 Sep 2024 S1. Every wording below, oldest first.

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  1. Question 1

    14 Jul 2023 S1

    62
    If m∠C=m∠Zm\angle C = m\angle Z and AC=XZ, then which of the following conditions is necessary for ΔABC\Delta ABC and ΔXYZ\Delta XYZ to be congruent?

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  2. Question 2

    12 Sep 2024 S1

    67
    In triangles ABC and DEF, AB = FD and ∠A=∠D\angle A = \angle D. The two triangles are congruent by SAS criterion if:

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