Download Triangle Similarity

Spi.4.11 Use basic theorems about similar and
congruent triangles to solve problems.
Check.4.36 Use several methods, including AA,
SSS, and SAS, to prove that two triangles are
similar.
CLE 3108.4.8 Establish processes for
determining congruence and similarity of
figures, especially as related to scale factor,
contextual applications, and transformations.
""Thunder
is good, thunder is impressive; but it is lightning that does the work." Mark Twain
Angle-Angle (AA)
Similarity
Side-Side-Side (SSS)
Similarity
Side-Angle –Side
(SAS) Similarity
If the two angles of one triangle
are congruent to two angles of
another triangle, then the
triangles are similar. PT and
QS then PQRTSU
If the measures of corresponding
sides of two triangles are
proportional, then the triangles
are similar.
Ex. PQ/ST= QR/SU=RP/UT so
PQRTSU
If the measures of two sides of a
triangle are proportional to the
measure of two corresponding
sides of another triangle and the
included angles are congruent,
then the triangles are similar.
Ex. PQ/ST= QR/SU and QS
then PQRTSU
Q
S
R
P
T
U
Q
c
a
R
b
P
S
ax
T
R
P
T
U
bx
Q
c
a
cx
S
ax
cx
U
In the figure, FGEG, BE=15, CF=20, AE=9 and
DF=12. Determine which triangles are similar.
C
If you can show AE & BE proportional to
DF and CF, then SAS Similarity to show triangles
as similar
B
G
A
F
FGE is an isosceles triangle so GFE  GEF
E
D
Two are proportional
So ABE  DCF
In the figure, AB||DC, BE=27, DE = 45, AE = 21,
CE=35. Determine which two triangles are
similar
CDE EBA because they are alternate interior angles
C
BEA CED, because they are vertical angles
ABE  CDE, because AA Similarity
Check
B
E
A
D
 Find
AE and DE
C
A
x -1
2
Since AB|| CD
ABEDCE and BAECDE
because alternate interior angles
B
E
5
x+5
D
ABE~DCE because of AA similarity
ABE~DCE because of AA similarity
2(x+5) = 5(x – 1)
2x + 10 = 5x – 5
15 = 3x
5=x
EA = x – 1 = 5 – 1 = 4
DE = x + 5 = 5 + 4 = 9
0.9 x = 1.2(240)
0.9x = 288
x = 288/.9=320
2 x = 12(242)
2x = 2904
x = 1452
Actual height 1450
 Page
479, 10 – 24 even
 Notebook
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