Transcript 7.3: Similar Triangles

Homework Questions:
If you have questions on any of the following
homework assignments, please write the
problem number on the board.
• 7.1 worksheet
• 7.2 textbook
p.473-476 #12-13, 19-18, 27-28, 35-37, 51
• “Something Fishy” packet
7.3: Similar Triangles
Objectives:
I will be able to…
1. Identify similar triangles
2. Recognize similar triangles in real life
Angle-Angle (AA) Similarity
Postulate
If two angles of one triangle are
congruent to two angles of another
triangle, then the two triangles are similar.
If K  Y and J  X, then
 JKL   XYZ.
K
Y
L
Z
X
J
Side-Side-Side (SSS)
Similarity Theorem
If the corresponding sides of two
triangles are proportional, then the
triangles are similar.
If
AB
BC
CA, then ABC ~  PQR
=
=
PQ
QR
RP
A
P
Q
B
C
R
Side-Angle-Side (SAS)
Similarity Theorem
If an angle of one triangle is congruent to an
angle of a second triangle, and the lengths of
the sides including these angles are
proportional, then the triangles are similar.
If mX  mM and
ZX
XY

,
PM MN
X
thenXYZ ~ MNP.
M
P
Z
Y
N
Are the triangles below similar? If yes,
write the similarity statement and what
similarity postulate/theorem you used.
W
X
V
Y
Z
If AC = 6, AD = 10, BC = 9, CE = 6, is
ACB ~ DCE?
A
E
C
D
B
What is the scale factor?
What theorem/postulate did you use?
L
33
M
Are the triangles similar?
106°
N
20
36°
Q
30
P
Write the similarity statement.
Find the scale factor.
Find MN.
11:10
MN = 22
Homework:
– p.483-484 #9, 11, 17-23
A 6.5 ft tall car standing next to an adult
elephant casts a 33.2 ft shadow. If the adult
elephant casts a shadow that is 51.5 ft long
then how tall is the elephant?
Indirect Measurement:
On a windy day, you notice another student outside in the front of the
school whose jacket has been carried up to the top of the flagpole. As you
watch this student attempt to climb the flagpole to retrieve their jacket you
start to wonder exactly how tall the flagpole is. Since you have plenty of
time to ponder as you are watching the student climb you begin to realize
things… You notice that you are exactly 6 feet tall and you are currently
casting (as your friend tells you by walking from heel to toe) a three foot
shadow. You then figure out that the flagpole is casting an 18 foot shadow.
Assuming that the sun’s rays are forming the same angle on you and the
flagpole, what is the height of the flagpole?