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11 (a) Are these triangles definitely congruent? Give a reason - OCR - GCSE Maths - Question 11 - 2019 - Paper 4
Question 11
11 (a) Are these triangles definitely congruent? Give a reason. Not to scale Triangle ABC: - Angle A = 36° - Angle B = 80° - Angle C = 64° Triangle DEF: - Angle D... show full transcript
Worked Solution & Example Answer:11 (a) Are these triangles definitely congruent? Give a reason - OCR - GCSE Maths - Question 11 - 2019 - Paper 4
Step 1
Are these triangles definitely congruent? Give a reason.
Answer
No, the triangles are not necessarily congruent. The angles of both triangles are known, but the lengths of the sides are not provided. Therefore, it is possible that the triangles could either be congruent or similar. Without knowing the lengths or other properties, we cannot definitively state that they are congruent.
Step 2
Prove that these two triangles are congruent.
Answer
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Angle-Angle-Angle (AAA): Since both triangles have the same angle measures, specifically, angle A = angle D = 36°, angle B = angle E = 80°, and angle C = angle F = 64°, they are similar by AAA.
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Corresponding Angles: The angles are identical, therefore angle [GHI] = angle [LJK].
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Side-Angle-Side (SAS): If we know a corresponding side (for example, GH = JK) and the included angles, we can state that the two triangles can be proven congruent by the SAS criterion.
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Moreover, since the angles across from equal sides must also be equal, this shows that the triangles are indeed congruent.