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 115°. What do the other three angles measure?

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

3. A regular pentagon has how many degrees in each interior angle?

72°

108°

120°

144°

Show your working:

🧩 Part 2: Multi-Step Problem Solving

4. A rectangular garden is 12 metres long and 8 metres wide. A path 1.5 metres wide runs around the entire perimeter. What is the area of the path only?

Step 1 - Identify what you know:

Step 2 - Plan your solution:

Step 3 - Calculate:

Final Answer: The area of the path is ____________ square metres.

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

Answer: ____________ centimetres

Explain your reasoning: ___________________________________________________

💭 Part 3: Critical Thinking & Justification

6. Sarah claims that all rectangles are squares. Is she correct? Justify your answer with examples.

7. Extension Challenge: A quadrilateral has angles of 2x°, 3x°, 4x°, and 5x°. Find the value of x and determine what type of quadrilateral this could be.

Value of x: ____________

The four angles are: ______°, ______°, ______°, ______°

This quadrilateral could be a: ___________________________________

8. Real-World Application: An architect needs to design a triangular roof section. Two sides measure 8 metres and 6 metres, with an angle of 120° between them. Describe the steps you would take to find the length of the third side.