Same chapter3 marksDifficulty: Medium
Explain why SSA is not a valid criterion for the congruency of two triangles.
Triangles
3 marksDifficulty: Medium
Prove that the angles opposite to the equal sides of an isosceles triangle are equal.
Original Khojo Papers practice question — not from a past board paper.
Answer
Draw the bisector of the vertex angle to meet the base. The two triangles formed have the two equal sides, the common bisector and the equal included angles, so they are congruent by SAS, and the base angles are corresponding angles of congruent triangles and therefore equal.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
The converse is also true: if two angles of a triangle are equal, the sides opposite them are equal.
Related questions
From the same topic and chapter, at a similar level.
Same chapter3 marksDifficulty: Medium
In triangle ABC, AB = AC and D is the midpoint of BC. Prove that AD is perpendicular to BC.
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Same chapter3 marksDifficulty: Medium
In triangles ABC and PQR, AB = PQ, BC = QR and angle B = angle Q. State the criterion by which the triangles are congruent and name three pairs of equal parts that follow.
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Same chapter3 marksDifficulty: Medium
In an isosceles triangle ABC, AB = AC and ∠A = 40°. Find ∠B and ∠C.
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Same chapter2 marksDifficulty: Easy
State the four conditions of congruency of two triangles.
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Same chapter1 markDifficulty: Easy
Two triangles are congruent by the RHS rule when:
Triangles