Question

Determine whether triangles ACB and AEF are similar. Show your working and explain your reasoning.

(Hint: First draw them as separate triangles. Then decide whether the triangles are similar by showing Angle-Angle Similarity, Side-Angle-Side Similarity, or Side-Side-Side Similarity)

Answer 1

Explanation:

It is assumed EF and CB are parallel.

The triangles ACB and AEF are similar by SAS as:

• CAB is common angle
• AC and AE overlap
• AB and A F overlap

Confirm if corresponding sides have same ratios:

• AC / AE = AB / A F
• (8 + 4) / 8 = (10 + 5) / 10
• 12/8 = 15/10
• 1.5 = 1.5

Confirmed