Triangles
ICSE · Class 9 · Mathematics
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Two triangles ABC and DEF have AB = DE = 6 cm, BC = EF = 4 cm, and ∠B = ∠E = 60°. By which congruence criterion are they congruent?
In a triangle, the sum of any two sides must be:
If in triangle PQR, ∠P = 70° and ∠Q = 50°, find ∠R:
In an isosceles triangle ABC with AB = AC, if ∠A = 40°, find ∠B:
Sample Questions
Which of the following are valid congruence criteria for triangles? (Select all that apply)
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SSS, SAS, ASA, RHS
Valid congruence criteria are: SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), AAS (Angle-Angle-Side), and RHS (Right angle-Hypotenuse-Side). AAA only ensures similarity, not congruence. SSA is not a valid criterion as it can lead to ambiguous cases.
The exterior angle of a triangle is 120°. If one of the interior opposite angles is 50°, find the other interior opposite angle:
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70°
By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles. So: Exterior angle = Sum of two opposite interior angles. 120° = 50° + other angle. Therefore, other angle = 120° - 50° = 70°.
If triangle ABC ≅ triangle PQR, and AB = 5 cm, BC = 7 cm, which of the following must be true?
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PQ = 5 cm, QR = 7 cm, ∠A = ∠P, Area of ABC = Area of PQR
When triangles are congruent (ABC ≅ PQR), corresponding parts are equal: AB = PQ = 5 cm, BC = QR = 7 cm, ∠A = ∠P, ∠B = ∠Q (not ∠R), ∠C = ∠R. Congruent triangles have equal areas.
A triangle can have at most how many obtuse angles?
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1
A triangle can have at most one obtuse angle. If a triangle had two obtuse angles, their sum would exceed 180° (since each obtuse angle > 90°), but the sum of all three angles in a triangle must be exactly 180°. Therefore, maximum one obtuse angle is possible.
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