Class 9 Isosceles Triangles Mock Test (ICSE)

Topics in Isosceles Triangles

• Angles opposite equal sides are equal
• Converse of the isosceles triangle theorem
• Problems and proofs on isosceles triangles

Isosceles Triangles practice questions with answers

1. Q1Multiple choice·1 mark
   In $\triangle ABC$, $AB = AC$. The exterior angle formed by producing $BC$ to $D$ at vertex $C$ is $120^\circ$. The measure of $\angle A$ is:

   1. (a)$60^\circ$
   2. (b)$120^\circ$
   3. (c)$30^\circ$
   4. (d)$50^\circ$
   Show answer and step marks

   1. Correct option: (a) $60^\circ$+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   In $\triangle ABC$, $AB = AC$ and $\angle B = 70^\circ$. The measure of $\angle A$ is:

   1. (a)$55^\circ$
   2. (b)$40^\circ$
   3. (c)$140^\circ$
   4. (d)$70^\circ$
   Show answer and step marks

   1. Correct option: (b) $40^\circ$+1

   Answer: (b)
3. Q3Multiple choice·1 mark
   In a triangle $XYZ$, if $\angle Y = \angle Z = 55^\circ$, then the relation between the sides is:

   1. (a)$XY \neq XZ$
   2. (b)$XY = XZ$
   3. (c)$XY = YZ$
   4. (d)$XZ = YZ$
   Show answer and step marks

   1. Correct option: (b) $XY = XZ$+1

   Answer: (b)
4. Q4Short answer·2 marks
   In $\triangle ABC$, $\angle B = \angle C = 50^\circ$. If $AB = 7.5\text{ cm}$, find the length of $AC$ and state the theorem used.
   Show answer and step marks

   1. States that the sides opposite to equal angles of a triangle are equal (Converse of the isosceles triangle theorem).+1
   2. Concludes that $AC = AB = 7.5\text{ cm}$.+1

   Answer: $AC = 7.5\text{ cm}$; theorem: sides opposite equal angles of a triangle are equal (converse of the isosceles triangle theorem).

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