Question

Will give you a medal and become a fan ; )
In ΔABC shown below...
BD|BA = BE|BC
The flow chart 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? (5 points)
Answers:

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 1

@borak can you please help?

Answer 2

If two corresponding sides of two triangles are in proportion, and their included angles have the same measure, then the triangles are similar

Answer 3

you in the question have the two sides proportion are the same

Answer 4

DBC and ABC are similars .; then you just need to find the angle that in the two triangles is equal ;

Answer 5

@borak So I believe A and A are equal am I wrong?

Answer 6

why you choose this one ?

Answer 7

1. ∠ A ≅ ∠ A
2. Reflexive Property of Equality @borak you said i had to find the one that is equal so it is either that or B and B

Answer 8

what is the angle that in the Both tiangles is equals ?

Answer 9

the proportion sides is given data , you just have to find the equal (one) angle in the Both triangles

Answer 10

the next step written ( SIDE-Angel-SIDE) the two side are given ;
you just have to find angle

Answer 11

@borak 1. ∠ A ≅ ∠ B
2. Corresponding Angles Postulate ?

Answer 12

A = A // A not angle in BDE
this not true

Answer 13

Corresponding Angles Postulate ?
this occur if DE || AC , then you can talk this

Answer 14

What is the aswer @borak

Answer 15

But you have to proof this , even this right ; not these angles is the equal;
it's D and A

Answer 16

What? it did a bunch of questions marks

Answer 17

the last one is the right , B is exist in the two triangles in the same angle;
according to Refelxivity the B =B ; then we find angle that are equal

Answer 18

So you mean this?

Answer 19

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

Answer 20

@borak

Answer 21

yea ?/ the answer is B =B

Answer 22

which is that

Answer 23

out of my 4 answers

Answer 24

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 25

you have it the last one :D

Answer 26

Okay thanks