Warm-Up Exercises
ANSWER 8
1. Give the postulate or theorem that justifies why the triangles are similar.
2. Solve = .1632
12 – x x
ANSWER AA Similarity Postulate
Warm-Up ExercisesEXAMPLE 1 Find the length of a segment
In the diagram, QS || UT , RS = 4, ST = 6, and QU = 9. What is the length of RQ ?
SOLUTION
Triangle Proportionality Theorem
Substitute.
Multiply each side by 9 and simplify.RQ = 6
RQQU
RSST=
RQ 9
46=
Warm-Up ExercisesEXAMPLE 2 Solve a real-world problem
On the shoerack shown,AB = 33 cm, BC = 27 cm, CD = 44 cm,and DE = 25 cm, Explain why the gray shelf is not parallel to the floor.
Shoerack
SOLUTION
Find and simplify the ratios of lengths determined by the shoerack.
CBBA
2733= 9
11=CD
DE4425=
Warm-Up ExercisesEXAMPLE 2 Solve a real-world problem
Because , BD is not parallel to AE .
So, the shelf is not parallel to the floor.
4425
911=
ANSWER
Warm-Up ExercisesGUIDED PRACTICE for Examples 1 and 2
1. Find the length of YZ .
31511ANSWER
2. Determine whether PS || QR .
ANSWER parallel
Warm-Up ExercisesEXAMPLE 3 Use Theorem 6.6
In the diagram, 1, 2, and 3 are all congruent and GF = 120 yards, DE = 150 yards, and CD = 300 yards. Find the distance HF between Main Street and South Main Street.
City Travel
SOLUTION
Corresponding angles are congruent, so FE, GD , and HC are parallel. Use Theorem 6.6.
Warm-Up Exercises
HG + GF GF
CD + DE DE=
EXAMPLE 3
HGGF
CDDE= Parallel lines divide transversals
proportionally.
Property of proportions (Property 4)
Substitute.
HF = 360
HF120
300+150 150=
450150
HF120 = Simplify.
Multiply each side by 120 and simplify.
The distance between Main Street and South Main Street is 360 yards.
Use Theorem 6.6
Warm-Up Exercises
SOLUTION
EXAMPLE 4 Use Theorem 6.7
In the diagram, QPR RPS. Use the given side lengths to find the length of RS .
~
Because PR is an angle bisector of QPS, you can apply Theorem 6.7. Let RS = x. Then RQ = 15 – x.
Warm-Up ExercisesEXAMPLE 4 Use Theorem 6.7
7x = 195 – 13x Cross Products Property
x = 9.75 Solve for x.
RQRS
PQPS=
15 – x x
= 73
Angle bisector divides opposite side proportionally.
Substitute.
Warm-Up ExercisesGUIDED PRACTICE for Examples 3 and 4
Find the length of AB.
3.
ANSWER 19.2
4. ANSWER 24
Warm-Up ExercisesDaily Homework Quiz
Find the value of the variable.
1.
ANSWER 12
Warm-Up ExercisesDaily Homework Quiz
Find the value of the variable.
2.
ANSWER 13.5
Warm-Up ExercisesDaily Homework Quiz
Find the value of the variable.
3.
ANSWER 23.8
Warm-Up ExercisesDaily Homework Quiz
4. This diagram represents a tract of land being developed for homes. Which lot has the greatest perimeter?
ANSWER Lot C