Download Proving triangles similar

Z
Warm Up
W
7.5
U
12
5
V X
Y
6
XYZ
1. UVW ~  ____
2. What is the scale factor of UVW to XYZ 6/5 or
1.2
3. What is VW ? 10
4. What is XZ ? 9
5. If mU  50 and mY  30, what is mZ ?
100
Shadow Math
Jeannie is practicing on the basketball goal outside her house. She thinks that
the goal seems lower than the 10 ft. goal she plays on in the gym. She
wonders how far the goal is from the ground. Jeannie can not reach the goal
to measure the distance to the ground, but she remembers something from
math class that may help. First, she needs to estimate the distance from the
bottom of the goal post to the top of the backboard. To do this, Jeannie
measures the length of the shadow cast by the goal post and backboard.
She then stands a yardstick on the ground so that it is perpendicular to the
ground, and measures the length of the shadow cast by the yardstick. Here
are Jeannie’s measurements:
Length of shadow cast by goal post and backboard: 5 ft. 9 in. (69 in.)
Length of yardstick’s shadow: 1 ft. 6 in. (18 in.)
If the goal is approximately 24 in. from the top of the backboard, how does the height
of the basketball goal outside Jeannie’s house compare to the one in the gym? Justify
your answer.
Questions over hw?
3 Ways to Prove
Triangles Similar
Angle-Angle (AA~) Similarity Postulate
Being able to show that two angles in one
triangle are congruent to two angles of the
other triangle
D
A
B
E
F
C
Side-Side-Side (SSS~) Similarity THM
Being able to show that the measures of all the
corresponding sides of the triangles are
proportional.
D
A
E
F
AB BC CA


DE EF
FD
B
C
Side-Angle-Side (SAS~) Similarity THM
Being able to show that the measure of
two pair of corresponding sides are
proportional AND the included angles are
congruent
D
A
F
E
AB BC

DE EF
B
C
Ex. Determine whether the triangles are similar. If
so, tell which similarity test is used and complete
the statement.
68°
43°
68°
43°
V
Y
7
W
11
3
U
X
5
Z
Prove that RST ~ PSQ
1. Two sides are proportional
SAS~2. Included angle is congruent
S
4
P
12
R
5
16 20

4
5
4 4

1 1
Q
15
T
S  S
reflexive