1. 7.5 Proportions and Similar Triangles
Textbook pg 386

2. Side-Side-Side Similarity Theorem
If the corresponding sides of two triangles are proportional, then the triangles are similar 4 8 5 10 6 12 = = A
Since the sides are proportional,
By SSS ~
ABE ~ ACD 6 4 5 B E 6 4 10 D C

3. Side-Angle-Side Similarity Theorem
If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides that include these angles are proportional, then the triangles are similar 21 14 10 15 A E D C B
Since 2 pairs of corresponding sides are proportional and the included angles are congruent
By SAS ~
ABC ~ DBE
vertical
angles 21 14 15 10 =

4. Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally. 20 24
24 – c 15 12 c 9

5. Converse of the Triangle Proportionality Theorem
If a line divides two sides of a triangle proportionally, then that line is parallel to the third side IF 12 21 8
THEN 14

6. Midsegment Theorem
The segment that connects the midpoints of two sides of a triangle is parallel to the third side and half as long 10
midpoint 4
midpoint x 10 4 15

7. 12 x

8. Homework # 6
Pg 390
Problems 1-9
You must write the problems