Question

Given:
In ∆ABC, (line)DE||(line)AC
Prove:
BD over BA = BE over BC

Answer 1

The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.

Answer 2

Statements:
1. (line)DE||(line)AC
2. (line)BA is a transversal that intersects two parallel lines
3.______
4. ∡B≅∡B
5. ∆ABC ~ ∆DBE
6._______
Reasons:
1. Given
2. Conclusion from statement 1
3._______
4. Reflexive property of equality
5. Angle-Angle (AA) similarity postulate
6.________

Answer 3

line 3, <BDE is congruent <BAC because of corresponding angles.

Answer 4

So
Statement 3: <BDE is congruent <BAC
Reason 3: Corresponding angles.?

Answer 5

that is correct

statement 6 would then be what you want to prove (since the last line is usually what you want to prove, otherwise, you'd need more lines)

Answer 6

so statement 6 would be

BD/BA = BE/BC

Answer 7

So what would be the reasoning for BD/BA = BE/BC?

Answer 8

well if two corresponding pairs sides are in proportion, then the triangles must be similar

this idea probably has many names, but I managed to find one (not sure if it's the official name) here:

http://web.archive.org/web/20071027112302/http://regentsprep.org/Regents/mathb/1b/theorems.htm

The name on that page is the Side Proportionality rule or property

Answer 9

Yes, my teacher uses SP property. Thank you for the help

Answer 10

np