Question

(03.06 MC)

In AABC shown below,
A
BD BE
BA BC
Given
B
48 = 48
Reflexive Property
of Equality
BD BE
BA BC
The following flowchart proof with missing statements and reasons proves that if a line intersects two
sides of a triangle and divides these sides proportionally, the line is parallel to the third side:
E
2
с
4BDE 4BAC
Corresponding
Parts of Similar
Triangles
DE || AC
Converse of the
Corresponding
Angles Postulate
Which reason can be used to fill in the numbered blank space?

Answer 1

The blanks are filled with

1. Δ ABC ~ Δ DBE

2. Side Angle Side similarity theorem

What is Side Angle Side similarity theorem

The SAS similarity theorem states if an angle of one triangle is congruent to an angle of another triangle, and the included sides (the sides between the angles) are proportional, then the two triangles are similar.

The parts used in the proof includes

Side: AB ~ DB

Angle: ∠ B ≅ ∠ B

Side: BC ~ BE

The sides are proportional while the angles are congruent