Isosceles: Real-world Applications
Mathematics
Grade 6
12 questions
~24 mins
1 views0 downloads
About This Worksheet
This worksheet explores the properties of isosceles triangles through real-world scenarios, calculations, and reasoning tasks suitable for Grade 6 students.
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Isosceles: Real-world Applications
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
An isosceles triangle has two equal sides. If the vertex angle measures 40°, what are the measures of the base angles?
[3 marks]2.
Calculate the unknown angle in an isosceles triangle where the two equal angles are each 55°.
[2 marks]3.
Construct an isosceles triangle with a vertex angle of 60° and equal sides of 5 cm. What are the base angles?
[3 marks]B
Problem Solving & Reasoning
Tackle these multi-step problems carefully. Show your reasoning.
1.
A flagpole casts a shadow that forms a 30° angle with the ground. The shadow is 4 meters long. The flagpole and the shadow form an isosceles triangle with the ground. How tall is the flagpole?
[4 marks]2.
In an isosceles triangle, the two equal sides are each 8 cm. The base is 10 cm. Find the measure of the vertex angle.
[3 marks]C
Real-world Applications
Apply your understanding to these real-life scenarios.
1.
A carpenter designs a mirror frame that is an isosceles triangle. The two equal sides are 15 cm each, and the base is 20 cm. If the carpenter wants to find the angles of the frame, what are the base and vertex angles?
[4 marks]2.
A kite is shaped as an isosceles triangle with two equal sides of 9 meters. The angles at the base are 45°. What is the measure of the top angle?
[3 marks]D
Challenge & Extension
Attempt these challenging problems to deepen your understanding.
1.
Prove that in an isosceles triangle, the angles opposite the equal sides are equal. Describe the reasoning process.
[4 marks]2.
Design an isosceles triangle where the vertex angle is 50°, and each side of the equal sides is 7 cm. Calculate the length of the base using the Law of Cosines.
[4 marks]E
Mixed Review
Answer these questions to review your knowledge of isosceles triangles.
1.
An isosceles triangle has sides of 6 cm, 6 cm, and 8 cm. Is it possible for the triangle to be equilateral? Explain.
[3 marks]2.
Plot an isosceles triangle with sides of 5 cm, 5 cm, and a base of 8 cm on the grid.
[3 marks]F
Error Analysis
Identify and correct the mistakes in the following: In an isosceles triangle, the two equal sides are 7 cm each, and the vertex angle is 50°, but the base angles are given as 60° each. What's wrong?
1.
Explain the mistake and provide the correct base angles.
[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