Express a ratio in simplest form'

1
Chapter 7

• Express a ratio in simplest form.
• State and apply the properties of similar
  polygons.
• Use the theorems about similar triangles.

2
Lecture 1 (7-1)

• Objectives
• Express a ratio in simplest form
• Solve for an unknown in a proportion

3
Ratio

• A comparison between numbers

5 7
5 7 s 5 t
4
Proportion

• An equation containing two ratios

5
Homework Set Lecture 1

• 7-1 1-35 odd (honors)
• 7-1 1-29 odd (regular)
• Worksheet

6
Lecture 2 (7-2,7-3)

• Objectives
• Express a given proportion in an equivalent form.
• State and apply the properties of similar
  polygons.

7
Means and Extremes

• The extremes of a proportion are the first and
  last terms
• The means of a proportion are the middle terms

a b c d
8
Properties of Proportion (POP)
is equivalent to
9
More POP
10
Similar Polygons

• All angles congruent
• All sides in proportion

A
D
F
E
B
C
11
The Scale Factor

• The reduced ratio between any pair of sides or
  the perimeters

12
Homework Set Lecture 2

• 7-2 1-37 odd
• 7-3 1-35 odd
• Worksheet

13
Lecture 3 (7-4, 7-5)

• Objectives
• Use the postulates and theorems to prove
  triangles are similar.

14
Postulate 15 (AA)

• If two angle of one triangle are congruent to two
  angles of another triangle, then the triangles
  are similar.

A
D
F
E
B
C
15
Theorem 7-1 (SAS)

• If an angle of a triangle is congruent to an
  angle of another triangle and the sides including
  those angles are proportional, then the triangles
  are similar.

A
D
F
E
B
C
16
Theorem 7-2 (SSS)

• If the three sides of one triangle are
  proportional to the three sides of another
  triangle, then the triangles are similar.

A
D
F
E
B
C
17
Homework Set Lecture 3

• Worksheet
• 7-4 1-27 odd
• 7-5 1-19 odd

18
Lecture 4 (7-6)

• Objectives
• Apply the Triangle Proportionality Theorem and
  its corollary
• State and apply the Triangle Angle-bisector
  Theorem

19
Divided Proportionally

• If points are placed on segments AB and CD so
  that , then we say that these
• segments are divided proportionally.

B
D
X
Y
A
C
20
Theorem 7-3

• If a line parallel to one side of a triangle
  intersects the other two sides, it divides them
  proportionally.

Y
B
A
X
Z
21
Corollary

• If three parallel lines intersect two
  transversals, they they divide the transversal
  proportionally.

R
W
S
X
T
Y
22
Theorem 7-4

• If a ray bisects an angle of a triangle, then it
  divides the opposite side into segments
  proportional to the other two sides.

Y
W
X
Z
23
Homework Set Lecture 4

• Worksheet
• 7-6 1-23 odd