Photo AI

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

Prove that angles are equal: ∠ABE and ∠CDE

96%

114 rated

Answer

Since AB is parallel to CD and AE and BE are transversals, by the Alternate Interior Angles Theorem, we have:

$∠ABE = ∠CDE$ .

Step 2

Prove that angles are equal: ∠BAE and ∠ECD

99%

104 rated

Answer

Similarly, since AB is parallel to CD, we can use the same theorem. Thus:

$∠BAE = ∠ECD$ .

Step 3

Establish the similarity of the triangles

96%

101 rated

Answer

Since we have shown that:

$∠ABE = ∠CDE$ $∠BAE = ∠ECD$ ,

it follows that triangles ABE and CDE have two pairs of angles equal. Therefore, by the Angle-Angle (AA) criterion, triangles ABE and CDE are similar:

$\triangle ABE \sim \triangle CDE$ .

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;