Isosceles: Challenge & Extension
Mathematics
Grade 8
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the properties and applications of isosceles triangles, designed for challenge and extension at Grade 8 level.
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Full preview • 11 questions
Isosceles: Challenge & Extension
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Introduction
1.
An isosceles triangle has at least two equal sides. The angles opposite these sides are also equal. Remember the isosceles triangle theorem when solving these problems.
[2 marks]B
Fluency & Practice
Calculate the missing lengths and angles in the following questions.
1.
In an isosceles triangle, the two equal sides each measure 7 cm. If the base angles are 50° each, find the vertex angle.
[3 marks]2.
An isosceles triangle has sides of length 10 cm and 10 cm, with a base of 14 cm. Calculate the height drawn to the base.
[3 marks]3.
Calculate the length of the equal sides if the vertex angle of an isosceles triangle is 40° and the base angles are equal.
[3 marks]C
Problem Solving & Reasoning
Solve the following multi-step problems and explain your reasoning.
1.
A triangle is isosceles with sides of length 12 cm. The vertex angle measures 60°. Find the length of the equal sides using trigonometry.
[4 marks]2.
Explain why the base angles of an isosceles triangle are equal, and provide a proof using the properties of isosceles triangles.
[4 marks]D
Real-world Applications
Apply your understanding of isosceles triangles to these contexts.
1.
A bridge design uses an isosceles triangle to support a span. The equal sides are 8 meters each, and the base is 10 meters. Calculate the angle between the supports at the top.
[3 marks]E
Challenge & Extension
Tackle these advanced problems requiring deeper reasoning.
1.
Construct an isosceles triangle where the equal sides are 9 cm, and the base angles are 70°. Find the length of the base.
[4 marks]2.
Given an isosceles triangle with a vertex angle of 30°, find the lengths of the equal sides if the base is 8 cm, using the Law of Cosines.
[4 marks]F
Mixed Review & Error Analysis
Identify and correct the mistakes in the following scenarios.
1.
A student claims that in an isosceles triangle, the two equal sides are always longer than the base. Is this true? Explain your reasoning.
[2 marks]2.
A triangle with sides 5 cm, 5 cm, and 9 cm is labeled as isosceles. Identify the mistake and correct the triangle's classification.
[2 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.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet