Question

Use ΔABC below to answer the question that follows:

Which fact is not used to prove that ABC is similar to DBE?

The sum of angles A and B are supplementary to angle C.

Segments AC and DE are parallel.

AB is a transversal line passing AC and DE.

Angle B is congruent to itself due to the reflexive property.

Answer 1

Two triangles can be similar by AAA,ASA ,SSS ,SAS property of similarity.

To prove triangles ABC similar to DBE we consider

Segments AC and DE are parallel.

AB is a transversal line passing AC and DE.

Angle B is congruent to itself due to the reflexive property.

The option which is not used to prove that ABC is similar to DBE is the first option :

The sum of angles A and B are supplementary to angle C.

Answer 2

Explanation:

To prove Δ ABC similar to ΔDBE we can consider

Segments AC and DE are parallel.

⇒ DE intersects AB and BC in same ratio.

AB is a transversal line passing AC and DE.

⇒∠BAC=∠BDE [corresponding angles]

Angle B is congruent to itself due to the reflexive property.

All of them are telling a relation of parts of ΔABC to ΔDBE.

The only option which is not used to prove that ΔABC is similar to ΔDBE is the first option ,"The sum of angles A and B are supplementary to angle C".