🧠 Part 1: Problem Analysis

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

67°

77°

87°

97°

2. Justify your answer: Explain which geometric rule you used and why it applies.

3. In a parallelogram, one angle measures 110°. Which statements are true? (Select all that apply)

The opposite angle also measures 110°

The adjacent angles measure 70°

All angles are equal

Opposite angles are supplementary

4. A regular hexagon has interior angles of _______ each. Show your working:

🔍 Part 2: Multi-Step Problem Solving

5. Complex Problem: Triangle ABC is similar to triangle DEF with a scale factor of 3:2. If the perimeter of triangle ABC is 24 centimetres, what is the perimeter of triangle DEF?

Step 1 - Identify what you know:

Step 2 - Plan your solution strategy:

Step 3 - Show your calculations:

Step 4 - Justify your reasoning:

6. Critical Evaluation: A student claims that all rectangles are squares. Analyse this statement and explain whether it's correct or incorrect, providing geometric reasoning.

🎯 Part 3: Extension Challenge

7. Design Challenge: Create a geometric problem involving at least two different geometric concepts (e.g., angles, similarity, transformations). Write the problem and provide the solution with full justification.

Your Problem:

Your Solution with Justification:

8. Real-World Application: Explain how the geometric reasoning skills you've used today could be applied in a real-world career (e.g., architecture, engineering, design, navigation).