7-5: Parts of Similar Triangles

1
7-5 Parts of Similar Triangles

• Expectations
• G1.2.5 Solve multi-step problems and proofs
  about the properties of medians, altitudes and
  perpendicular bisectors to the sides of a
  triangle and the angle bisectors of a triangle.
• G2.3.4 Use theorems about similar triangles to
  solve problems with and without the use of
  coordinates.

2
Proportional Perimeters Theorem

• If two triangles are similar, then the ratio of
  corresponding perimeters is equal to the ratio of
  corresponding sides.

3
Proportional Perimeters Theorem
4

• If ?ABC ?XYZ, AB 15, XY 25 and the
  perimeter of ?XYZ 45, what is the perimeter of
  ?ABC?

5
Corresponding Altitudes Theorem

• If two triangles are similar, then the ratio of
  corresponding altitudes is equal to the ratio of
  corresponding sides.

6
Corresponding Altitudes Theorem
7
If ?CDE ?KLM, determine the value of x.
M
16
8
K
L
8
Corresponding Angle Bisectors Theorem

• If two triangles are similar, then the ratio of
  corresponding angle bisectors is equal to the
  ratio of corresponding sides.

9
Corresponding Angle Bisectors Theorem
10
The triangles below are similar and AD and EH are
angle bisectors. Determine the perimeter of ?EHG.
11
Corresponding Medians Theorem

• If two triangles are similar, then the ratio of
  corresponding medians is equal to the ratio of
  corresponding sides.

12
Corresponding Medians Theorem
13

• ?ABC ?XYZ. If the perimeter of ?XYZ is half as
  much as the perimeter of ?ABC, and AD and XU are
  medians, determine the length of XU.

X
A
22
Z
U
Y
C
D
B
14
Angle Bisector Theorem

• An angle bisector of a triangle separates the
  opposite side into segments that have the same
  ratio as the other two sides.

15
Angle Bisector Theorem
16
Determine the value of x in the figure below.
24
x
14
12
17
Assignment

• pages 373 377, 13 33 (odds), 43, 47-57
  (all).