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
State that angle ABC = angle BCD
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Given that the angle ABC is equal to angle BCD, we can denote both angles as
∠ABC=∠BCD.
State that AB = CD
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From the question, we have that the lengths of sides AB and CD are equal:
AB=CD.
State that BC = AC with reason: BC = AC (common)
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Triangles ABC and BCD share side BC, hence:
BC=BC,
which is common to both triangles.
Conclude proof by stating triangles \triangle ABC \cong \triangle BCD with reason SAS and \angle C = \angle D
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By the Side-Angle-Side (SAS) criterion for triangle congruence, the two triangles are congruent:
△ABC≅△BCD.
Thus, from this congruence, we conclude that:
AC=BD.
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