Isosceles: Challenge & Extension
Mathematics
Grade 8
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the properties of isosceles triangles, including angles, proofs, and real-world applications, with extension and challenge questions.
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Isosceles: Challenge & Extension
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Answer the following questions to practice basic properties of isosceles triangles. Show your working in the grid spaces provided.
1.
In an isosceles triangle, the two equal sides each measure 10 cm. If the vertex angle is 40°, find the base angles.
[3 marks]2.
An isosceles triangle has two equal sides of length 12 cm and a vertex angle of 50°. Calculate the length of the base (using an approximate method).
[3 marks]3.
True or False: In an isosceles triangle, if the base angles are equal, then the sides opposite these angles are also equal.
[1 mark]4.
Construct an isosceles triangle with sides 8 cm, 8 cm, and base 10 cm. Mark all angles.
[4 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems involving isosceles triangles. Provide detailed explanations.
1.
A triangle is isosceles with equal sides of length 15 cm. The vertex angle measures 60°. Find the area of the triangle.
[4 marks]2.
Two sides of an isosceles triangle are 9 cm each. The base is 12 cm. Verify whether the triangle exists and find its angles.
[4 marks]C
Real-world Applications
Apply your understanding of isosceles triangles to solve these contextual word problems.
1.
A bridge design uses an isosceles triangle for support. The two equal sides are 20 meters each, and the vertex angle is 30°. Find the length of the base and explain how this helps in design stability.
[4 marks]D
Challenge & Extension
Attempt these advanced questions to extend your understanding of isosceles triangles.
1.
Prove that in an isosceles triangle, the angles opposite the equal sides are equal, using geometric theorems.
[4 marks]2.
Given an isosceles triangle with side lengths 7, 7, and x, find the range of possible values for x so that the triangle exists.
[3 marks]E
Mixed Review
Solve these mixed review questions to consolidate your knowledge of isosceles triangles.
1.
An isosceles triangle has equal sides of length 9 cm. If one of the base angles is 70°, find the vertex angle.
[3 marks]2.
Construct an isosceles triangle where the base angles are 55°, and the sides adjacent to the base are 14 cm. Mark all angles.
[4 marks]F
Error Analysis
Review the following common mistakes related to isosceles triangles and identify or correct them.
1.
A student claims that in an isosceles triangle, the base angles are always 45°. Explain why this is incorrect and give a correct statement.
[3 marks]2.
Identify and correct the mistake: 'In an isosceles triangle with sides 10 cm, 10 cm, and 8 cm, the base angles are both 40°.'
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet