Geometry Problem Solving Workshop

Name:

Date:

Geometric shapes and problem solving illustration

🧠 Part 1: Problem Analysis

1. A triangle has angles measuring 65° and 48°. What is the third angle?

Justification: Explain which geometric rule you used: ____________________

2. In a parallelogram ABCD, angle A measures 110°. Find the measures of the other three angles.

Angle B = ______° Angle C = ______° Angle D = ______°

3. Which strategy would you use FIRST to solve a complex geometry problem?

Start calculating immediately

Identify what is known and unknown

Draw a new diagram

Look up formulas

📐 Part 2: Multi-Step Problem Solving

4. A rectangular garden is 12 metres long and 8 metres wide. A diagonal path cuts across it. Calculate the length of the diagonal path and explain your reasoning.

Theorem used: ________________________________________________

Answer: The diagonal path is ____________ metres long.

5. Two similar triangles have a ratio of corresponding sides of 3:5. If the smaller triangle has a perimeter of 24 centimetres, what is the perimeter of the larger triangle?

Step-by-step reasoning:

🎯 Part 3: Critical Thinking & Justification

6. Sarah claims that all rectangles are squares. Is she correct? Justify your answer using geometric properties.

7. A regular hexagon has an interior angle sum of 720°. Without using a calculator, explain how you could find the measure of each interior angle.

Each interior angle measures: ____________°

8. Extension Challenge: Design your own geometry problem that requires at least two different geometric rules to solve. Write the problem and provide the solution with full justification.

Success Criteria Check: Tick when you have achieved each goal:

I identified knowns and unknowns in each problem

I applied appropriate geometric rules and theorems

I justified my methods using mathematical language

I showed persistence when problems were challenging