Angles and Shapes Properties

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Date:

Geometric shapes and angles illustration

📐 Part 1: Triangle Classification and Properties

1. A triangle has sides of 5 cm, 5 cm, and 8 cm. What type of triangle is this?

Equilateral

Isosceles

Scalene

Right-angled

2. Which of the following are properties of an equilateral triangle? (Select all that apply)

All sides are equal

All angles are 60°

Has one right angle

Has three lines of symmetry

3. Triangle ABC has angles measuring 45°, 90°, and 45°. Classify this triangle by both its angles and sides.

By angles: _________________ triangle

By sides: _________________ triangle

4. What is the minimum information needed to prove two triangles are congruent using SAS?

🔄 Part 2: Transformations and Similarity

5. Triangle PQR is translated 4 units right and 3 units up. If point P is at (2, 1), what are the coordinates of P' after the translation?

P' = ( _____ , _____ )

6. When a shape is reflected across the y-axis, what happens to the coordinates?

The x-coordinate changes sign, y-coordinate stays the same

The y-coordinate changes sign, x-coordinate stays the same

Both coordinates change sign

Both coordinates stay the same

7. Two similar triangles have corresponding sides in the ratio 3:5. If the smaller triangle has a perimeter of 18 cm, what is the perimeter of the larger triangle?

8. In similar triangles ABC and DEF, if AB = 6 cm, BC = 8 cm, and DE = 9 cm, find the length of EF.

🧠 Part 3: Reasoning and Extension

9. Proof Challenge: Triangle XYZ has XY = XZ and angle YXZ = 40°. Prove that angles XYZ and XZY are equal, and find their measures. Show your working and reasoning.

10. Extension: A regular hexagon is rotated about its centre. What is the minimum angle of rotation needed for the hexagon to map onto itself?

Minimum rotation angle: _________°

Explain your reasoning:

11. Advanced Problem: Two triangles are similar with a scale factor of 2:3. If the area of the smaller triangle is 12 cm², what is the area of the larger triangle? Explain the relationship between linear scale factor and area scale factor.

12. Investigation: Draw or describe a quadrilateral that has exactly two lines of symmetry. Name the shape and explain why it has this property.