The table shows four pairs of triangles. For each pair, decide whether the two triangles are mathematically similar. Write each answer, yes or no, in the second column of the table. Triangles Not to scale 1st Pair: A triangle with angles: 60°, 70°, and 50° A triangle with angles: 70°, 50°, and 60° 2nd Pair: A triangle with sides 6 cm, 3 cm, and 7 cm A triangle with sides 12 cm, 14 cm, and 6 cm 3rd Pair: A triangle with sides 3 cm, 4 cm, and 5 cm A triangle with sides 5 cm, 12 cm, and 13 cm 4th Pair: A triangle with sides 3 cm, 5 cm, and 6 cm A triangle with sides 6 cm, 10 cm, and a common angle of 70° Mathematically similar? (yes/no) 1st Pair: 2nd Pair: 3rd Pair: 4th Pair:

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The table shows four pairs of triangles - OCR - GCSE Maths - Question 11 - 2023 - Paper 3

Question 11

The table shows four pairs of triangles. For each pair, decide whether the two triangles are mathematically similar. Write each answer, yes or no, in the second col... show full transcript

Worked Solution & Example Answer:The table shows four pairs of triangles - OCR - GCSE Maths - Question 11 - 2023 - Paper 3

Step 1

1st Pair: Are the triangles mathematically similar?

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Answer

Yes, the angles match (60°, 70°, 50°) in both triangles, confirming their similarity.

Step 2

2nd Pair: Are the triangles mathematically similar?

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Answer

No, the side lengths do not maintain the same ratios: Ratio of sides in Triangle 1: 6/3 = 2, 7/3 = 2.33. Ratio of sides in Triangle 2: 12/6 = 2, 14/6 eq 2.33.

Step 3

3rd Pair: Are the triangles mathematically similar?

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Answer

Yes, Triangle 1 is a right triangle (3 cm, 4 cm, 5 cm) and Triangle 2 (5 cm, 12 cm, 13 cm) shares a right angle; they follow the properties of similar triangles.

Step 4

4th Pair: Are the triangles mathematically similar?

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Answer

No, the angles match (70°, 70°) but the ratio of the other sides does not confirm similarity. For Triangle 1: Ratio of sides 3 cm, 6 cm, 5 cm (to 6 cm) is not equal to Triangle 2.

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The table shows four pairs of triangles - OCR - GCSE Maths - Question 11 - 2023 - Paper 3

Worked Solution & Example Answer:The table shows four pairs of triangles - OCR - GCSE Maths - Question 11 - 2023 - Paper 3

1st Pair: Are the triangles mathematically similar?

2nd Pair: Are the triangles mathematically similar?

3rd Pair: Are the triangles mathematically similar?

4th Pair: Are the triangles mathematically similar?

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