Download 7.3 Proving Triangles Similar

7.3 Proving Triangles Similar
SWBAT:
•  Use AA,SAS and SSS similarity statements.
•  Apply AA, SAS, and SSS similarity statements
Remember Triangle Congruence…
•  Remember the shortcuts we learned in order to
prove congruence in triangles?
•  We didn’t have to show 3 pairs of corresponding
angles congruent and 3 pairs of corresponding
sides congruent.
•  We could use SSS, SAS, ASA, AAS or the HL
Theorem to show congruence quickly.
Same Idea with Similarity!
•  We do not always have to show triangles are
similar by using the definition of Similarity.
•  We can use these Postulates and Theorems as
shortcuts to prove similarity.
AA~ Postulate
Think…
Why does the postulate only require TWO pairs or
corresponding congruent angles for Angle Angle
Similarity?
•  If we know two pairs of corresponding angles are congruent
then we know the third corresponding pair must be congruent
also!
Using the AA~ Postulate
•  Are these Triangles Similar? How do you know?
•  If similar write a Similarity Statement
•  Can a Similarity Ratio be determined? Why or why not?
Yes, the triangles are Similar by AA~
ΔRSW~ΔVSB
A Similarity Ratio cannot be determined because there are no side
measures to compare.
You Try…
•  Explain why the
Triangles are Similar
then write a Similarity
Statement
AB ⊥ MX
So as long as we know two Angles…
•  Just knowing that two pairs of Corresponding
Angles are congruent, is enough information to
prove two triangles similar.
•  There are other Theorems that can also be
utilized to prove Similarity.
SAS~ Theorem
SSS~ Theorem
Using Similarity Theorems
•  Are the Following Two
Triangles Similar?
QR 3
=
XY 4
PR 6 3
= =
ZY 8 4
ΔQRP~ΔXYZ by SAS~
Theorem
∠QRP ≅ ∠XYZ
Both are Right Angles
Try this…
Explain why the
Triangles must be
Similar
Applying AA, SAS, and SSS Similarity
ABCD is a Parallelogram…
• Find WY
Indirect Measurement
•  We can use Similar Triangles to measure
distances that are difficult to measure directly.
•  This is called an Indirect Measurement
Another Indirect Measurement…
•  Mrs. McPherson is in the
Desert.
•  She is 6 ft. tall and casts a
4 ft. shadow. A cactus has
a 9ft shadow. How tall is
the Cactus?
Think…
Create…
More Similar Triangles…
TS TU
=
TR TV
x
5
=
x +16 5 +10
x
5
=
x +16 15
15(x) = 5(x +16)
15x = 5x + 80
10x = 80
x =8
Find y…
CM CN
=
CB CA
12
10
=
12 + y 10 + 6
12
10
=
12 + y 16
10(12 + y) = 12(16)
120 +10y = 192
10y = 72
y = 7.2
Solve for x!
x
2
=
13− x + x 2 + 3
x 2
=
13 5
5x = 26
26
x=
5
x = 5.2