ABCD is a quadrilateral - Edexcel - GCSE Maths - Question 21 - 2017 - Paper 1
Question 21
ABCD is a quadrilateral.
AB = CD.
Angle ABC = angle BCD.
Prove that AC = BD.
Worked Solution & Example Answer:ABCD is a quadrilateral - Edexcel - GCSE Maths - Question 21 - 2017 - Paper 1
Step 1
State that angle ABC = angle BCD
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Answer
Given that angle ABC is equal to angle BCD, we can denote these angles as equal in our proof.
Step 2
State that AB = CD
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Answer
It is given that AB is equal to CD, which will allow us to establish a relationship between the corresponding sides of triangles.
Step 3
Link with reason: BC = BC (common)
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Answer
Since BC is a common side in both triangles ABC and BCD, we can state that BC = BC.
Step 4
Conclude proof by stating triangles ABC and BCD are congruent
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Answer
We can conclude that triangles ABC and BCD are congruent by the SAS (Side-Angle-Side) postulate, as we have established two pairs of equal sides and the angle between them. Therefore, it follows that AC = BD.
