F-pattern: Challenge & Extension
Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A challenging worksheet focusing on the F-pattern of corresponding angles formed by parallel lines and a transversal, designed for Year 9 extension students.
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F-pattern: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Review the F-pattern formed when a transversal crosses parallel lines. Remember that the corresponding angles are equal when the lines are parallel, forming an 'F' shape. Use this pattern to solve for unknown angles and analyze related problems.
B
Fluency & Practice
Answer the following questions to practice the basic properties of the F-pattern.
1.
Given two parallel lines cut by a transversal, if the corresponding angle is 65°, find the measure of its matching corresponding angle.
[2 marks]2.
If one corresponding angle is 110°, what is the measure of the alternate interior angle on the same transversal?
[2 marks]3.
Construct a pair of parallel lines with a transversal such that a corresponding angle is 75°. Mark the angles on your diagram.
[3 marks]C
Targeted Practice
Apply your understanding of the F-pattern to solve these questions.
1.
In the diagram, the angle at position A (corresponding with the angle at C) is 68°. Find the measure of the angle at D assuming lines are parallel.
[2 marks]2.
Two parallel lines are cut by a transversal. If the corresponding angles at one point are 120° and 60°, identify which angles are which and justify your answer.
[3 marks]3.
Calculate the value of x if the corresponding angles in the diagram are given as 3x + 10° and 2x + 30°, and the lines are parallel.
[3 marks]4.
Construct a diagram with two parallel lines cut by a transversal, where the corresponding angles are in a ratio of 2:3, and the larger angle measures 75°. Find all angles involved.
[4 marks]D
Problem Solving & Reasoning
Solve these multi-step problems involving the F-pattern and explain your reasoning.
1.
A transversal intersects two parallel lines. If one angle is 3x + 20° and its corresponding angle is 2x + 10°, and both are on the same side, find the value of x and the angles.
[4 marks]2.
In a real-world context, a fence has two parallel sections, and a diagonal support crosses both. If the angles at the support are labeled as 4x° and 2x + 15°, and the fence sections are parallel, find x and the angles.
[4 marks]E
Real-world Applications
Apply the F-pattern principles to solve these contextual problems.
1.
A city planner designs a park with parallel walkways crossed by a diagonal path. If the angles formed where the path crosses the walkways are 70°, find the measure of the corresponding angles along the walkways.
[3 marks]F
Challenge & Extension
Tackle these advanced problems that extend your understanding of the F-pattern.
1.
Given a diagram with two parallel lines cut by a transversal, the angles labeled are 3x°, 2x + 10°, and 5x - 20°. Determine x and all missing angles, explaining your steps.
[4 marks]2.
Prove that in a figure with parallel lines cut by a transversal, the sum of a corresponding angle and its alternate interior angle equals 180°. Use the F-pattern properties to justify your proof.
[4 marks]G
Mixed Review & Error Analysis
Review the concepts by identifying common misconceptions and solving mixed questions.
1.
A student states that all corresponding angles are 90° in a diagram with parallel lines and a transversal. Is this correct? Explain your reasoning and correct any mistake.
[3 marks]2.
Calculate the missing angle in a diagram where the angles are labeled as 2x, 3x + 20°, and 4x - 10°, and the lines are parallel. Show your work.
[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.
- • 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