Geometry Problem Solving Workshop

Name:

Date:

🧠 Part 1: Problem Analysis

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

Justification: Explain which geometric rule you used and why it applies here.

2. In a regular hexagon, each interior angle measures:

108°

120°

135°

144°

Show your working:

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

Answer: _________ cm

4. Which of these statements about congruent triangles are correct? (Select all that apply)

They have the same shape and size

Corresponding angles are equal

They must be in the same position

Corresponding sides are equal

📐 Part 2: Multi-Step Problem Solving

5. A rectangular garden is 12 metres long and 8 metres wide. A path 1.5 metres wide runs around the entire outside edge of the garden.

a) What are the dimensions of the garden including the path?

Length: _________ metres Width: _________ metres

b) What is the area of just the path (not including the garden)?

Answer: _________ square metres

6. Problem-Solving Strategy: A quadrilateral has three angles measuring 85°, 92°, and 108°.

Step 1 - Identify what you know and what you need to find:

Step 2 - Choose your method and solve:

Step 3 - Justify your answer using geometric rules:

🎯 Part 3: Critical Thinking Challenge

7. Extension Problem: Two circles with centres 10 cm apart have radii of 3 cm and 5 cm respectively. Describe the relationship between these circles and justify your reasoning.

8. Create Your Own Problem: Design a geometry problem that requires at least two different geometric rules to solve. Include the solution.

Your Problem:

Your Solution with Justification:

9. Reflection: What was the most challenging part of today's problems? What strategy helped you the most?