📐 Part 1: Triangle Classification by Sides and Angles

1. Classify each triangle by its sides. Choose the correct answer:

Triangle A: sides 6cm, 6cm, 6cm

Equilateral

Isosceles

Scalene

2. A triangle has angles measuring 30°, 60°, and 90°. This triangle is:

Acute triangle

Right triangle

Obtuse triangle

3. Which properties can a triangle have? (Check all that apply)

Two equal sides and one right angle

Three equal sides and three acute angles

All different side lengths and one obtuse angle

Four equal angles

4. Complete the classification table by filling in the missing information:

Triangle with sides 4cm, 7cm, 9cm:

Classification by sides: ________________

Triangle with angles 45°, 45°, 90°:

Classification by angles: ________________

Classification by sides: ________________

📏 Part 2: Measuring and Drawing Triangles

5. Using a ruler and protractor, measure the triangle below and classify it:

Side lengths: _____ cm, _____ cm, _____ cm

Angle measurements: _____°, _____°, _____°

Classification by sides: ________________

Classification by angles: ________________

6. Draw and label the following triangles in the space provided:

a) An equilateral triangle with sides of 5cm each

b) A right-angled scalene triangle

7. Explain your reasoning: Why is it impossible to have a triangle with angles measuring 60°, 70°, and 80°?

🧠 Part 3: Problem Solving and Reasoning

8. Sort the following triangles into the correct groups. Draw lines to match each triangle to its classification:

Triangle with sides 3cm, 4cm, 5cm

Triangle with angles 60°, 60°, 60°

Triangle with sides 8cm, 8cm, 12cm

Triangle with angles 30°, 60°, 90°

Equilateral triangle

Isosceles triangle

Right triangle

Scalene triangle

9. A builder is creating a triangular garden bed. If two sides measure 6 metres and 8 metres, and the angle between them is 45°, describe what type of triangle this will be and explain your reasoning:

10. Challenge: In te reo Māori, triangle is called "tapatoru". If you were explaining triangle classification to a friend, write a short explanation using the correct mathematical vocabulary: