📐 Part 1: Problem Analysis

1. A triangle has angles measuring 45° and 67°. What is the measure of the third angle?

68°

78°

88°

98°

2. Which geometric rules could you use to solve angle problems? (Select all that apply)

Angles in a triangle sum to 180°

Vertically opposite angles are equal

Co-interior angles are supplementary

Alternate angles are equal

3. A rectangle has a length of 12 cm and width of 8 cm. If it is enlarged by a scale factor of 1.5, what is the new perimeter?

Answer: ________ cm

4. In a parallelogram, one angle measures 110°. What do the other three angles measure?

🧠 Part 2: Multi-Step Problem Solving

5. A quadrilateral ABCD has parallel sides AB and DC. Angle A = 75° and angle B = 105°. Find angles C and D, then justify your reasoning using geometric properties.

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

Step 2: Show your calculations:

Step 3: Justify your answer using geometric rules:

6. 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? Explain your reasoning.

Explanation: ________________________________________________

Answer: ________ cm

⭐ Part 3: Extension Challenge

7. Design your own geometry problem involving at least two different geometric rules (e.g., angle properties and similarity). Write the problem below, then solve it and justify each step.

Your Problem:

Your Solution and Justification:

8. Reflect on your problem-solving process today. What strategies helped you most? What would you do differently next time?