parts of similar triangles
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PARTS OF SIMILAR TRIANGLES
• Recognize and use proportional relationships of corresponding perimeters of similar triangles.
• Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of
similar triangles.
JOHN B. CORLEY
PROPORTIONAL PERIMETERS THEOREM
If two triangles are similar, then the perimeters are proportional to the corresponding sides.
JOHN B. CORLEY
Example 1 – Perimeters of Similar Triangles
12
35
37
5
If ∆LMN ~ ∆QRS, QR = 35, RS = 37, SQ = 12, and NL = 5, find the perimeter of ∆LMN
JOHN B. CORLEY
N
MS
Q R
L
Example 1 – Perimeters of Similar Triangles, cont.
N
MS
Q R
L
12
35
37
5
Let x represent the perimeter of ∆LMN. The perimeter of ∆QRS = 35 + 37 + 12 or 84.
Perimeter = 84
JOHN B. CORLEY
Example 1 – Perimeters of Similar Triangles, cont.
N
MS
Q R
L
12
35
37
5
Let x represent the perimeter of ∆LMN. The perimeter of ∆QRS = 35 + 37 + 12 or 84.
Perimeter = 84
35
420128412
5
ofperimeter ofPerimeter
x
x
x
QRSLMN
SQNL
JOHN B. CORLEY
SPECIAL SEGMENTS OF SIMILAR TRIANGLES
Corresponding Altitudes
TUPQ
UVQR
TVPR
UWQA U
W V
AP R
Q
T
JOHN B. CORLEY
SPECIAL SEGMENTS OF SIMILAR TRIANGLES
Corresponding Angle Bisectors
TUPQ
UVQR
TVPR
UXQB
JOHN B. CORLEY
X
B
U
P R
Q
T
SPECIAL SEGMENTS OF SIMILAR TRIANGLES
Corresponding Medians
TUPQ
UVQR
TVPR
UYQM
Y
M
U
P R
Q
T V
JOHN B. CORLEY
Example 2 – Medians of Similar Triangles
∆ABC ~ ∆DEF
BG and EH are medians
BC = 30, BG = 15, EF = 15
Find EH
JOHN B. CORLEY
3015
15x
E
HF
GA C
B
D
Example 2 – Medians of Similar Triangles
∆ABC ~ ∆DEF
BG and EH are medians
BC = 30, BG = 15, EF = 15
Find EH
5.7
22530153015
x
xx
EFBC
EHBG
JOHN B. CORLEY
3015
15x
E
HF
GA C
B
D
Example 3 – Solve Problems with Similar Triangles
PHOTOGRAPHY
JOHN B. CORLEY
6.16 m35 mm 42 mm x
ANGLE BISECTOR THEOREM
BP R
Q
An angle bisector in a triangle separates the opposite side into segments that have the same ratio as the other two sides.
RQPQ
BRPB
JOHN B. CORLEY
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