7.8. Triangle Proportionality http://www.ck12.org
Given: 4 ABCwithDE||AC
Prove:ADDB=CEEB
TABLE7.2:
Statement Reason
1.DE||AC Given2.^61 ∼=^62 ,^63 ∼=^64 Corresponding Angles Postulate
3. 4 ABC∼4DBE AA Similarity Postulate
4.AD+DB=AB,EC+EB=BC Segment Addition Postulate
5.ABBD=BCBE Corresponding sides in similar triangles are propor-
tional
6.ADBD+DB=ECBE+EB Substitution PoE
7.ADBD+DBDB=ECBE+BEBE Separate the fractions
8.ADBD+ 1 =ECBE+ 1 Substitution PoE (something over itself always equals
- 9.ADBD=ECBE Subtraction PoE
Example A
A triangle with its midsegment is drawn below. What is the ratio that the midsegment divides the sides into?
The midsegment’s endpoints are the midpoints of the two sides it connects. The midpoints split the sides evenly.
Therefore, the ratio would bea:aorb:b. Both of these reduce to 1:1.
Example B
In the diagram below,EB||CD. FindBC.
Use the Triangle Proportionality Theorem.