Isosceles Triangles
ICSE · Class 9 · Mathematics
Most important questions from Isosceles Triangles for ICSE Class 9 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.
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Which of the following statements are true for an isosceles triangle? (Select all correct options)
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It has at least two equal sides, Angles opposite to equal sides are equal, The altitude from vertex angle bisects the base
An isosceles triangle has at least two equal sides (not necessarily all three). The fundamental property is that angles opposite to equal sides are equal. The altitude from the vertex angle to the base bisects the base at right angles. A triangle cannot have two right angles as the sum would exceed 180°.
If the vertex angle of an isosceles triangle is 120°, find each base angle.
True or False: In an isosceles triangle, the altitude, median, and angle bisector from the vertex angle to the base are the same line.
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True
This is true for isosceles triangles. The altitude from the vertex angle to the base also serves as the median (bisects the base), angle bisector (bisects the vertex angle), and perpendicular bisector of the base. This is a unique property of isosceles triangles.
In triangle XYZ, XY = XZ = 15 cm and ∠YXZ = 80°. Calculate the perimeter if YZ = 18 cm.
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