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The diagram shows four triangles - Edexcel - GCSE Maths - Question 5 - 2020 - Paper 1
Question 5
The diagram shows four triangles. Two of these triangles are congruent. Write down the letters of these two triangles. (Total for Question 4 is 1 mark)
Worked Solution & Example Answer:The diagram shows four triangles - Edexcel - GCSE Maths - Question 5 - 2020 - Paper 1
Step 1
Two of these triangles are congruent.
Answer
To determine which triangles are congruent, we can apply the criteria for triangle congruence. In this case, let’s analyze the angles and sides of the given triangles:
- Triangle A has angles of 55°, 45°, and 80° with sides 10 cm and 10 cm.
- Triangle B has angles of 45°, 55°, and a side of 8 cm opposite the 45° angle, making its validation slightly different due to side lengths.
- Triangle C has angles of 55°, 45°, and a side of 10 cm, opposite the 45° angle and a side of 8 cm.
- Triangle D has angles of 80°, 45°, and a side of 10 cm, which aligns suitably with the sides.
Upon comparison, Triangle A and Triangle D both have:
- Angles: 55° and 45° (with the remaining being 80° and additional sides matching).
- Both have a common side (10 cm) which satisfies the condition that the triangles are congruent.
Thus, the two triangles that are congruent are: A and D.