Geometry Problem Solving Challenges

Name:

Date:

Geometric shapes and problem solving illustration

📐 Part 1: Angle Problem Solving

1. In a regular octagon, what is the measure of each interior angle?

120°

135°

140°

144°

2. Two parallel lines are cut by a transversal. If one angle measures 68°, what could be the measure of a corresponding angle?

22°

68°

112°

180°

3. Show your working to find the unknown angle x in a triangle where the other two angles are 47° and 85°.

📏 Part 2: Similarity and Scaling

4. Two similar triangles have a scale factor of 1:3. If the smaller triangle has a perimeter of 12 cm, what is the perimeter of the larger triangle?

Answer: _______ cm

5. A photograph measuring 8 cm by 12 cm is enlarged by a scale factor of 2.5. Calculate the area of the enlarged photograph.

6. In two similar right-angled triangles, the hypotenuse of the smaller triangle is 5 cm and the hypotenuse of the larger triangle is 15 cm. If the shorter leg of the smaller triangle is 3 cm, what is the length of the shorter leg in the larger triangle?

Length: _______ cm

🧠 Part 3: Problem Solving Challenge

7. A rectangular garden bed is 4 metres by 6 metres. A path of uniform width is built around the outside of the garden bed, increasing the total area to 48 square metres. What is the width of the path?

8. Explain your problem-solving strategy for question 7. What geometric principles did you use?

9. Extension Challenge: Create your own geometry problem involving either angle relationships or similarity. Include the solution.

10. Reflect on your problem-solving approach today. Which geometric concepts did you find most useful and why?