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.
