📐 Triangles: Congruence and Properties

Questions in this quiz

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1. Question 1

   If two triangles have all three pairs of corresponding sides equal, the triangles are congruent by the SSS (Side-Side-Side) criterion.

2. Question 2

   Which of the following is NOT a valid criterion for proving two triangles congruent?

3. Question 3

   In triangle $ABC$, if $AB = 5$ cm, $BC = 7$ cm, and $\angle B = 60°$, and triangle $DEF$ has $DE = 5$ cm, $EF = 7$ cm, and $\angle E = 60°$, then triangles $ABC$ and $DEF$ are congruent by the ___ criterion.

4. Question 4

   When two triangles are congruent, their corresponding angles are always equal.

5. Question 5

   In a right-angled triangle, the RHS (Right angle-Hypotenuse-Side) congruence criterion requires which three elements to be equal?

6. Question 6

   Triangle $PQR$ is congruent to triangle $XYZ$ such that $\angle P = \angle X$, $\angle Q = \angle Y$, and PR = ___.

7. Question 7

   Two isosceles triangles both have a vertex angle of $80°$ and equal legs of length $6$ cm. Are these triangles necessarily congruent?

8. Question 8

   If two triangles have two pairs of equal corresponding angles, they are always congruent.

9. Question 9

   In right triangle $ABC$ with right angle at $C$, if the hypotenuse $AB = 13$ cm and one leg $AC = 5$ cm, then the other leg $BC = ___ cm.

10. Question 10

    In triangles $ABC$ and $PQR$, it is given that $AB = PQ$, $\angle A = \angle P$, and $\angle B = \angle Q$. Which congruence criterion proves that $\triangle ABC \cong \triangle PQR$?