1. 7.4-APPLYING PROPERTIES OF SIMILAR TRIANGLES
2/4/13

2. Bell Work 2/4 Solve each proportion. 1. 2. AB = 16 QR = 10.5 3. 4.
AB = 16
QR = 10.5
x = 21
y = 8

3. Theorem 1

4. Example 1
Find US.
It is given that , so by the Triangle Proportionality Theorem.
Substitute 14 for RU,
4 for VT, and 10 for RV.
Cross Products Prop.
US(10) = 56
Divide both sides by 10.

5. Example 2 Find PN. Use the Triangle Proportionality Theorem.
Substitute in the given values.
2PN = 15
Cross Products Prop.
PN = 7.5
Divide both sides by 2.

6. Theorem 2

7. Example 3
Verify that
Since , by the Converse of the Triangle Proportionality Theorem.

8. Example 4 AC = 36 cm, and BC = 27 cm. Verify that .
Since , then by the Converse of the
Triangle Proportionality Theorem.

9. Corollary 1

10. Example 5
Suppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch.

11. Example 5 continued 4.5(LM) = 4.9(2.6) Cross Products Prop.
AB = 4.5 in.
BC = 2.6 in.
CD = 4.1 in.
KL = 4.9 in.
Given
2-Trans. Proportionality Corollary
Substitute 4.9 for KL, 4.5 for AB, and 2.6 for BC.
Cross Products Prop.
4.5(LM) = 4.9(2.6)
Divide both sides by 4.5.
LM  2.8 in.

12. Example 5 continued 2-Trans. Proportionality Corollary
Substitute 4.9 for KL, 4.5 for AB, and 4.1 for CD.
Cross Products Prop.
4.5(MN) = 4.9(4.1)
Divide both sides by 4.5.
MN  4.5 in.

13. Example 6 Use the diagram to find LM and MN to the nearest tenth.
LM  1.5 cm
MN  2.4 cm

14. Theorem 3

15. Example 7 Cross Products Property 40(x – 2) = 32(x + 5)
Find PS and SR.
by the ∆  Bisector Theorem.
Substitute the given values.
Cross Products Property
40(x – 2) = 32(x + 5)
Distributive Property
40x – 80 = 32x + 160

16. Example 7 continued 40x – 80 = 32x + 160 Simplify. 8x = 240
Divide both sides by 8.
x = 30
Substitute 30 for x.
PS = x – 2
SR = x + 5
= 30 – 2 = 28
= = 35

17. Example 8 Find AC and DC. by the ∆  Bisector Theorem.
Substitute in given values.
Cross Products Theorem
4y = 4.5y – 9
Simplify.
–0.5y = –9
Divide both sides by –0.5.
y = 18
So DC = 9 and AC = 16.