Triangles — Practice Quiz
Gujarat Board · Class 9 · Mathematics
Try a 4-question quiz on Triangles for Gujarat Board Class 9 Mathematics: tap an answer to check it and see why. 44 questions in the full chapter test.
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Quick Quiz: Triangles
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In triangle ABC, AB = 5 cm, BC = 7 cm, and AC = 8 cm. In triangle PQR, PQ = 5 cm, QR = 7 cm, and PR = 8 cm. Which congruence rule proves that triangle ABC ≅ triangle PQR?
In an isosceles triangle, if one of the base angles is 65°, what is the measure of the vertex angle?
In triangle PQR, PQ = 8 cm, angle P = 60°, and PR = 6 cm. In triangle XYZ, XY = 8 cm, angle X = 60°, and XZ = 6 cm. Calculate the length of the third side QR if the triangles are congruent.
In a right triangle ABC with right angle at C, if AC = 9 cm and BC = 12 cm, find the length of hypotenuse AB.
Sample Questions
Which of the following are valid congruence rules for triangles?
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SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), RHS (Right-Hypotenuse-Side)
Valid congruence rules are: SAS (two sides and included angle), ASA (two angles and included side), AAS (two angles and any side), RHS (for right triangles), and SSS (all three sides). SSA is not a valid congruence rule because it can result in two different triangles with the same measurements.
In triangle ABC, if AB = AC and angle B = 40°, find the measure of angle C.
Two right triangles have hypotenuses of 13 cm and one leg of 5 cm each. These triangles are congruent by RHS rule.
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True
The RHS (Right-Hypotenuse-Side) congruence rule states that if the hypotenuse and one side of a right triangle are equal to the hypotenuse and corresponding side of another right triangle, then the triangles are congruent. Since both triangles have the same hypotenuse (13 cm) and the same leg (5 cm), they are congruent by RHS rule.
Match the triangle types with their angle properties:
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Equilateral triangle - All angles are 60°
Equilateral triangle: All sides equal, so all angles equal 60°. Isosceles triangle: Two sides equal, so two angles equal. Right triangle: One angle is 90°. Scalene triangle: All sides different, so all angles different. This follows from the relationship between sides and angles in triangles.
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