Question

In ΔABC shown below, BD over BA equals BE over 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:
Which reason can be used to fill in the numbered blank space?

A) 1. ∠BDE ≅ ∠BAC
2. Corresponding Angles Postulate

B) 1. ∠BDE ≅ ∠BAC
2. Corresponding Parts of Similar Triangles

C) 1. ∠BDE ≅ ∠BCA
2. Alternate Exterior Theorem

D) 1. ∠BDE ≅ ∠BCA
2. Corresponding Parts of Similar Triangles

Answer 1

@Kirby123

Answer 2

B=B by the reflexive property

Answer 3

ok

Answer 4

1. ΔABC ~ ΔDBE
2. Side-Angle-Side Similarity Postulate

Answer 5

ok

Answer 6

1. ∠ A ≅ ∠ A
2. Reflexive Property of Equality
1. ∠ A ≅ ∠ B
2. Corresponding Parts of Similar Triangles
1. ∠ A ≅ ∠ B
2. Corresponding Angles Postulate
1. ∠ B ≅ ∠ B
2. Reflexive Property of Equality

Answer 7

4. ∠ A ≅ ∠ C; Isosceles Triangle Theorem
5. ΔBDE ~ ΔBAC; Angle-Angle (AA) Similarity Postulate

Answer 8

ok, thank you!

Answer 9

the answer is B =B

Answer 10

thank you