Question

Rectangle ABCD is shown with diagonal AC drawn. Point F is on AC and point E on DC such that FE is perpendicular to DC. Prove triangle ABC is similar to triangle CEF

Answer 1

Triangle ABC is similar to triangle CEF.

Explanation:

Diagram is inserted for the reference.

ABCD is a rectangle.

ABC is a right angled triangle because all the angles of the rectangle are 90◦ - (a)

CEF is a right angled triangle because FE is perpendicular to DC – (b)

In triangles ABC and CEF,

1. Angle ABC = Angle CEF = 90◦ (Both are right angles from a and b)

2. Angle BCA = Angle EFC (Alternate angles on parallel lines are equal on intersection)

Hence using Similarity property of AA (Angle, Angle), Triangle ABC and CEF are similar.