In the diagram AB is parallel to CD - OCR - GCSE Maths - Question 15 - 2019 - Paper 5
Question 15
In the diagram AB is parallel to CD.
AED and BEC are straight lines.
Prove that triangle ABE is similar to triangle CDE.
Worked Solution & Example Answer:In the diagram AB is parallel to CD - OCR - GCSE Maths - Question 15 - 2019 - Paper 5
Step 1
Using Corresponding Angles
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Answer
Since AB is parallel to CD, we can apply the Corresponding Angles Postulate.
Looking at the transversal AE, we have:
Angle ABE = Angle CDE (corresponding angles)
Angle AEB = Angle CED (also corresponding angles)
This indicates that the angles in triangles ABE and CDE are equal.
Step 2
Applying the AA Criterion for Similarity
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Answer
With the two pairs of corresponding angles being equal,
we can conclude by the AA (Angle-Angle) criterion that triangle ABE is similar to triangle CDE.
