Transcript Lesson 8

8-8
6th grade math
Similar Figures
Objective
• To use proportions to solve problems involving
similar figures
• Why? To know how to solve missing sides or
lengths of triangles, rectangles, etc. that are
similar in size.
California State Standards
NS 1.3 : Use proportions to solve problems (e.g…
find the length of a side of a polygon similar to a
known polygon) …
MR 2.4: Use a variety of methods, such as words,
numbers, symbols, … diagrams, … to explain
mathematical reasoning.
Vocabulary
• Similar figures
– Figures that have the same shape but not the same
size (congruent = same size and shape)
a
d
e
f
h
g
b
c
Rectangles: abcd ≈ efgh or abcd ~ efgh (similar to)
ab ≈ ef ; cd ≈ gh; bc ≈ fg; da ≈ he (corresponding sides or lengths). Sides’
lengths change.
∠a ≈ ∠e; ∠b ≈ ∠f; ∠c ≈ ∠ g; ∠d ≈ ∠ h (corresponding angles). Angles’
measurement always stay the same, no matter how the angles
change.
How to Solve Missing Sides of Similar
Figures
1) Locate corresponding
sides. Color coding each
corresponding side might
help you to ‘see’ better.
2) Write a proportion.
Corresponding sides make
one ratio. (AC/DF)
3) Solve.
* A short cut may be to
‘observe’ how the similar
figure was ‘enlarged’ or
‘decreased’ and multiply or
divide with that number.
Triangles are similar. abc ~ def
b
e
6
4
3
2
d x
f
a
8
c
ab ~ de
ac df
6 ~ 3
8
X
24 ÷ 6 = 4
df = 4
How to Solve Missing Angles of Similar
Figures
1) Locate corresponding
angles.
2) If finding a triangle’s
missing angle, remember
triangles angles add to
180°. If finding a
rectangle’s missing
angle, remember
rectangles add to 360°.
3) Add the angles and
subtract from either 180
(triangle) or 360
(rectangle).
Triangles are similar. abc ~ def
103̊
103̊
30̊
x
̊
180 – (103 + 30)
180 – 133 = 47°
Try It!
Quadrilateral KLMN ~ to
quadrilateral GHIJ.
1) m∠ K
2) HI
3) KN
H
110°
L 2” M
9”
3” 110°
K
70°N
G
12”
I
J
1) m∠ K = 360 - (110 + 110 + 70 + x)
360 – 270 = 70
2) HI =
LM = KL
2 = 3
HI GH
x 9
18 ÷ 3 = 6
HI = 6”
3) KN
GJ = GH
KN
KL
36 ÷ 9 = 4
KN = 4”
12 = 9
x
3
Objective Review
• To use proportions to
solve problems involving
similar figures
• Why? You now know how to solve
missing sides or lengths of triangles,
rectangles, etc. that are similar in
size.
• Use proportions to find missing sides
of similar figures.
• Write proportions with
corresponding part of similar figures.
Independent Practice
• Complete problems 511
• Copy original problem
first.
• Show all work!
• If time, complete Mixed
Review: 12-18
• If still more time, work
on Accelerated Math.