20 (a) Are these two triangles definitely congruent? Give a reason - OCR - GCSE Maths - Question 20 - 2019 - Paper 1
Question 20
20 (a) Are these two triangles definitely congruent? Give a reason.
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Worked Solution & Example Answer:20 (a) Are these two triangles definitely congruent? Give a reason - OCR - GCSE Maths - Question 20 - 2019 - Paper 1
Step 1
Are these two triangles definitely congruent? Give a reason.
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Answer
The two triangles are definitely congruent because they satisfy the Angle-Angle-Angle (AAA) criterion for similarity, where they have identical corresponding angle measures: 36°, 64°, and 80° in both triangles.
Step 2
Prove that these two triangles are congruent.
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Answer
To prove that triangles GHI and JKL are congruent, we can use the Side-Angle-Side (SAS) criterion.
Sides: Both triangles have one side of length 9 cm (GH = JK) and a second side of length 7 cm (GI = JL).
Angle: The angle between these sides in both triangles is 36° (∠GHI = ∠JKL).
Thus, by the SAS criterion, triangle GHI is congruent to triangle JKL.
