Explore · MATH-5B-C11-L03-OPEN
Classify a triangle with sides 7, 7, and 7 cm.
Great Inheritance Mathematics Term B · Original independent course
Classifying Triangles
Watch for: Calling a right triangle necessarily scalene.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C11-L03-PREREQ
Can sides 3, 4, and 5 cm form a triangle?
Show worked answer (after attempting)
Answer: Yes
The sum of every two lengths exceeds the third.
Understand the idea
Classify triangles by side lengths and angle types using valid examples and counterexamples. The essential earlier idea is: 5A measurement and angle reading, including correct degree labels and ruler use.. The model below will always use the actual quantities from the worked problem. Check calling a right triangle necessarily scalene when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C11-L03-Q01
Classify a triangle with sides 6, 6, and 6 cm.
Solution: equilateral
Check the triangle inequality. All are valid. All sides equal; so the triangle is equilateral.
Worked example 2 · MATH-5B-C11-L03-Q02
Explain why a triangle with side lengths 5, 5, 8 cm is isosceles.
Solution: isosceles
Check the triangle inequality. All are valid. Exactly two sides equal; so the triangle is isosceles.
Worked example 3 · MATH-5B-C11-L03-Q03
State whether sides 4, 6, 8 cm make an equilateral, isosceles, or scalene triangle.
Solution: scalene
Check the triangle inequality. All are valid. All three sides different; so the triangle is scalene.
Check understanding
1 · MATH-5B-C11-L03-Q04
Classify a triangle with sides 7, 7, and 7 cm.
Show worked answer (after attempting)
Answer: equilateral
Check the triangle inequality. All are valid. All sides equal; so the triangle is equilateral.
2 · MATH-5B-C11-L03-Q05
Explain why a triangle with side lengths 6, 6, 9 cm is isosceles.
Show worked answer (after attempting)
Answer: isosceles
Check the triangle inequality. All are valid. Exactly two sides equal; so the triangle is isosceles.
3 · MATH-5B-C11-L03-Q06
State whether sides 5, 7, 9 cm make an equilateral, isosceles, or scalene triangle.
Show worked answer (after attempting)
Answer: scalene
Check the triangle inequality. All are valid. All three sides different; so the triangle is scalene.
Guided practice
1 · MATH-5B-C11-L03-Q07
Classify a triangle with sides 8, 8, and 8 cm.
Show worked answer (after attempting)
Answer: equilateral
Check the triangle inequality. All are valid. All sides equal; so the triangle is equilateral.
2 · MATH-5B-C11-L03-Q08
Explain why a triangle with side lengths 7, 7, 10 cm is isosceles.
Show worked answer (after attempting)
Answer: isosceles
Check the triangle inequality. All are valid. Exactly two sides equal; so the triangle is isosceles.
3 · MATH-5B-C11-L03-Q09
State whether sides 6, 8, 10 cm make an equilateral, isosceles, or scalene triangle.
Show worked answer (after attempting)
Answer: scalene
Check the triangle inequality. All are valid. All three sides different; so the triangle is scalene.
4 · MATH-5B-C11-L03-Q10
Classify a triangle with sides 9, 9, and 9 cm.
Show worked answer (after attempting)
Answer: equilateral
Check the triangle inequality. All are valid. All sides equal; so the triangle is equilateral.
Independent practice
1 · MATH-5B-C11-L03-Q11
Explain why a triangle with side lengths 8, 8, 11 cm is isosceles.
Show worked answer (after attempting)
Answer: isosceles
Check the triangle inequality. All are valid. Exactly two sides equal; so the triangle is isosceles.
2 · MATH-5B-C11-L03-Q12
State whether sides 7, 9, 11 cm make an equilateral, isosceles, or scalene triangle.
Show worked answer (after attempting)
Answer: scalene
Check the triangle inequality. All are valid. All three sides different; so the triangle is scalene.
3 · MATH-5B-C11-L03-Q13
Classify a triangle with sides 10, 10, and 10 cm.
Show worked answer (after attempting)
Answer: equilateral
Check the triangle inequality. All are valid. All sides equal; so the triangle is equilateral.
4 · MATH-5B-C11-L03-Q14
Explain why a triangle with side lengths 9, 9, 12 cm is isosceles.
Show worked answer (after attempting)
Answer: isosceles
Check the triangle inequality. All are valid. Exactly two sides equal; so the triangle is isosceles.
5 · MATH-5B-C11-L03-Q15
State whether sides 8, 10, 12 cm make an equilateral, isosceles, or scalene triangle.
Show worked answer (after attempting)
Answer: scalene
Check the triangle inequality. All are valid. All three sides different; so the triangle is scalene.
6 · MATH-5B-C11-L03-Q16
Classify a triangle with sides 11, 11, and 11 cm.
Show worked answer (after attempting)
Answer: equilateral
Check the triangle inequality. All are valid. All sides equal; so the triangle is equilateral.
7 · MATH-5B-C11-L03-Q17
Explain why a triangle with side lengths 10, 10, 13 cm is isosceles.
Show worked answer (after attempting)
Answer: isosceles
Check the triangle inequality. All are valid. Exactly two sides equal; so the triangle is isosceles.
8 · MATH-5B-C11-L03-Q18
State whether sides 9, 11, 13 cm make an equilateral, isosceles, or scalene triangle.
Show worked answer (after attempting)
Answer: scalene
Check the triangle inequality. All are valid. All three sides different; so the triangle is scalene.
Challenge and error analysis
1 · MATH-5B-C11-L03-ERR1
The assigned question is: “Explain why a triangle with side lengths 13, 13, 16 cm is isosceles.” A learner wrote: “I ignored whether the given side lengths containing 13 satisfy the triangle inequality, and wrote scalene.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: isosceles
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: isosceles. Recompute from the given data: Check the triangle inequality. All are valid. Exactly two sides equal; so the triangle is isosceles.
2 · MATH-5B-C11-L03-ERR2
The assigned question is: “State whether sides 12, 14, 16 cm make an equilateral, isosceles, or scalene triangle.” A learner wrote: “I ignored whether the given side lengths containing 12 satisfy the triangle inequality, and wrote isosceles.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: scalene
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: scalene. Recompute from the given data: Check the triangle inequality. All are valid. All three sides different; so the triangle is scalene.
Exit check
Exit · MATH-5B-C11-L03-Q19
Classify a triangle with sides 12, 12, and 12 cm.
Show worked answer (after attempting)
Answer: equilateral
Check the triangle inequality. All are valid. All sides equal; so the triangle is equilateral.