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The diagram shows how a rhombus is made by joining two equilateral triangles - OCR - GCSE Maths - Question 6 - 2021 - Paper 3
Question 6
The diagram shows how a rhombus is made by joining two equilateral triangles. (a) Find the size of each interior angle of the rhombus. (b) The same rhombus can be ... show full transcript
Worked Solution & Example Answer:The diagram shows how a rhombus is made by joining two equilateral triangles - OCR - GCSE Maths - Question 6 - 2021 - Paper 3
Step 1
Find the size of each interior angle of the rhombus.
Answer
To find the interior angle of the rhombus formed by joining two equilateral triangles:
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Properties of an Equilateral Triangle: Each angle in an equilateral triangle measures 60°.
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Interior Angles of the Rhombus: The two angles that are formed at the vertices of the rhombus by the joining of two equilateral triangles can be calculated as:
- Each pair of equal angles in the rhombus leads to four congruent angles total, hence the total angle around a point is 360°.
- Each interior angle of the rhombus = rac{360°}{4} = 90°.
Therefore, each interior angle of the rhombus is 90°.
Step 2
Find the size of each angle of the isosceles triangle.
Answer
In the case of the isosceles triangles forming the rhombus:
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Understanding Isosceles Triangle Angles: Let's denote the equal angles as and the apex angle as .
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Total Angles of a Triangle: The sum of angles in any triangle is 180°:
- Hence, .
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Finding the angle A: Since the rhombus must also satisfy the angles:
- The apex angle corresponds to two 90° angles from the rhombus, thus .
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Solving for :
- Substitute back into the angle equation:
- .
Thus, the angles of the isosceles triangle are 45°, 45°, and 90°.