The diagram below shows two triangles - OCR - GCSE Maths - Question 11 - 2018 - Paper 1
Question 11
The diagram below shows two triangles.
Prove that triangle ABC is congruent to triangle ACD.
Worked Solution & Example Answer:The diagram below shows two triangles - OCR - GCSE Maths - Question 11 - 2018 - Paper 1
Step 1
angle BCA = 44°
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Answer
Given that angle A = 56° and angle B = 80°, we can find angle BCA. Since the angles in triangle ABC must sum to 180°, we have:
angleABC+angleBCA+angleA=180°
80°+angleBCA+56°=180°
Solving for angle BCA gives:
angleBCA=180°−80°−56°=44°
Step 2
angle DCA = 56°
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Answer
Similarly, to find angle DCA, we can use triangle ACD. We know angle ACD = 80°. Thus, we can find angle DCA using the same angle sum property:
angleACD+angleDCA+angleA=180°
80°+angleDCA+44°=180°
Solving for angle DCA gives:
angleDCA=180°−80°−44°=56°
Step 3
Side AC is common
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Answer
Both triangles share a side, AC. Thus, we have proven that:
angle BCA = 44°
angle DCA = 56°
side AC is common
This allows us to use the Angle-Side-Angle (ASA) criterion for triangle congruence, which states that if two angles and the side between them in one triangle are equal to two angles and the side between them in another triangle, then the triangles are congruent.
Therefore, we can conclude that triangle ABC is congruent to triangle ACD.
