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Triangle Side Classification
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Triangle Side Classification
Anahera, Georgia and Mele are designing triangular frames for kites. Classify each frame by its side lengths: equilateral has three equal sides, isosceles has exactly two equal sides, and scalene has no equal sides. For every set, first check that the lengths can form a triangle: the sum of the two shorter sides must be greater than the longest side.
Classify the Frames
Use side equality to classify the triangle. Include the triangle inequality check where asked.
1.Anahera’s frame has side lengths 8 cm, 8 cm and 8 cm. Classify it and explain how you know.
2.Georgia’s frame has side lengths 11 cm, 7 cm and 11 cm. Classify it and name the equal sides.
3.Mele’s frame has side lengths 6 cm, 8 cm and 9 cm. Which classification fits? Explain using the side lengths.
4.The festival team has four frame plans. Which plan is equilateral?
- A: 5 cm, 5 cm, 7 cm
- B: 9 cm, 9 cm, 9 cm
- C: 4 cm, 6 cm, 7 cm
- D: 10 cm, 10 cm, 15 cm
5.A frame is labelled 4 cm, 6 cm and 10 cm. Can these lengths make a triangle? Use the triangle inequality to justify your answer.
6.A frame has side lengths 5 cm, 5 cm and 9 cm. Is it a valid triangle, and if so, how is it classified? Show the inequality check.
7.True or false: Every isosceles triangle has exactly two equal sides, not three.
TrueFalse
8.Complete the rule: A scalene triangle has equal sides.
9.Georgia wants to make a scalene frame using whole-number lengths 5 cm, 7 cm and one other length. Give one possible length that makes a valid scalene triangle, and explain why it works.
10.A kite frame has two sides of 12 cm each. The third side is 24 cm. A designer calls it isosceles. Identify the problem with the design and state the correct conclusion.
Draw a triangle for the side lengths 5 cm, 6 cm and 7 cm. Label each side, then write its classification.
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