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Name the congruence rule (SSS, SAS, ASA, RHS) from the given equal parts

This type of question, asked 6 times: 9 Sep 2024 S2, 16 Sep 2025 S1, 19 Sep 2025 S1, 19 Sep 2025 S3, 21 Sep 2025 S2, 22 Sep 2025 S3. All 6 questions below, oldest first.

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  1. Question 1

    9 Sep 2024 S2

    52
    The points P and S are on the same side of the line segment QR, such that ∠PQR=90∘\angle PQR = 90^\circ, ∠SRQ=90∘\angle SRQ = 90^\circ and PQ=SRPQ = SR. Select the correct statement.

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  2. Question 2

    16 Sep 2025 S1

    70
    Two right-angled triangular blocks, ABC and DEF, have ∠B=∠E=90∘\angle B = \angle E = 90^\circ. If the lengths of the hypotenuses AC and DF are equal, and the sides AB and DE are equal, are the triangles congruent? If so, by what rule?

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  3. Question 3

    19 Sep 2025 S1

    70
    In a quadrilateral ABCD, a line segment BD is a diagonal such that AB=CD and ∠ABD=∠CDB\angle ABD = \angle CDB. Are the triangles ABD and CDB congruent? If so, by what rule?

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  4. Question 4

    19 Sep 2025 S3

    70
    In △ABC\triangle ABC, an angle bisector from A meets BC at D. If AD bisects ∠BAC\angle BAC, and AB=AC, are △ABD\triangle ABD and △ACD\triangle ACD congruent? If so, by what rule?

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  5. Question 5

    21 Sep 2025 S2

    70
    If in △LMN\triangle LMN and △OPQ\triangle OPQ, ∠L=∠O\angle L = \angle O, LM = OP, and ∠M=∠P\angle M = \angle P, which rule proves △LMN≅△OPQ\triangle LMN \cong \triangle OPQ?

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  6. Question 6

    22 Sep 2025 S3

    71
    Two triangles, △PQR\triangle PQR and △STU\triangle STU, have PQ=STPQ = ST, PR=SUPR = SU, and ∠QPR=∠TSU\angle QPR = \angle TSU. By what rule are they congruent?

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