Practice30Create account

Class 9 Properties of Isosceles Triangles — practice questions with answers

Geometry — Triangles · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. In an isosceles triangle, how many sides are equal in length?
Show answer
Answer: B) 2
By definition, an isosceles triangle has exactly two sides equal in length.
2. Which congruence rule is used to prove that base angles of an isosceles triangle are equal (AB = AC, with AD bisecting angle A)?
Show answer
Answer: A) SAS
With AB = AC, angle BAD = angle CAD, and AD common, triangles ABD and ACD are congruent by SAS.
3. In an isosceles triangle, an exterior angle at one base vertex is 110 deg. The vertex (apex) angle is (in degrees):
Show answer
Answer: A) 40
Base angle = 180 - 110 = 70 deg. Both base angles are 70, so apex = 180 - 140 = 40 deg.
4. In isosceles triangle ABC (AB = AC), the bisectors of the two base angles B and C meet at point I.
If the vertex angle A = 50 deg, find angle BIC, in degrees.
Show answer
Answer: A) 115
Base angles = = 65 deg each; half-angles = 32.5 deg. Angle BIC = 180 - (32.5 + 32.5) = 115 deg. (Also equals 90 + = 90 + 25 = 115.)
5. In triangle ABC, AB = AC. Point D lies on AC such that BD bisects angle B, and it is found that BD = BC.
Given that angle A = 36 deg, verify the figure by finding angle BDC, in degrees.
Show answer
Answer: A) 72
Base angles ABC = ACB = = 72 deg. In triangle BDC, BD = BC means it is isosceles with angle BDC = angle BCD = 72 deg.
Practise all 50 questions free →

10 free questions a day without an account — unlimited with a free account.