Download Ch. 17 Congruence and Similarity

17.1 Congruence and
Similarity
p. 374
Introduction:
Quick Review
Objective: to learn how to construct congruent line
segments and angles
Vocabulary:
• congruent = line segments and angles having the
same length or measure in degrees
Guided Learning:
Harcourt Math Glossary
How to construct a congruent LINE SEGMENT
How to construct a congruent ANGLE
17.2 Bisecting Line
Segments and Angles
p. 380
Introduction:
Quick Review
Objective: to learn how to bisect line segments and
angles by using a compass and ruler
Vocabulary:
• bisect = divide into TWO congruent parts
• midpoint = point halfway between the endpoints of a
line segment
• perpendicular bisector = line intersecting a line
segment at its midpoint to form a 90 degree angle
Harcourt Math Glossary
How to bisect an angle
Congruent and similar
shapes
Congruent
shapes
Similar
shapes
3
Congruent shapes
4
Start page
1. Which of these shapes are
congruent to the yellow one?
1
3
4
2
5
6
7
Hints
5
Answers
Start page
Congruent shapes are all shown in
yellow – were you right?
1
3
4
2
5
6
7
6
Start page
What makes a pair of shapes
“congruent”?
Same angles
Same side lengths
Can be rotated or a mirror image
A cut-out of one shape will always fit exactly
over the other
• Click the green box if you want to go back to
the first “congruent shapes” question page.
Question page
7
Start page
2. Which of these shapes are
congruent to the yellow one?
4
1
3
2
8
6
5
9
7
8
Answers
Start page
Congruent shapes are all shown in
yellow – were you right?
4
1
3
2
8
6
5
9
7
9
Similar shapes
10
Start page
Which of these shapes are similar
to the yellow one?
1
3
4
2
5
6
7
Hints
11
Answers
Start page
Similar shapes are all shown in
yellow – were you right?
1
3
4
2
5
6
7
12
Start page
What makes a pair of shapes
“similar”?
Same angles
Sides in the same proportion
Can be rotated or reflected
One is an enlargement of the other
Scale factor gives degree of enlargement:
– Scale factor 2 → size is doubled
– Scale factor 0.5 → size is halved
– Scale factor 1 → size doesn’t change → congruent too
• Click the green box if you want to go back to the
“similar shapes” question page.
Question page
13
Start page
Using similarity
Since shapes are similar, their
sides are in the same proportion
=> 6 = a
9
12
9cm
Multiply both sides by 12
=> 12 x 6 = a
9
6cm
=> a = 12 x 2 = 4 x 2
3
1
=> a = 8cm
12cm
a
14
Start page
Which of these shapes are similar
to the yellow one?
(They aren’t drawn to scale)
12
1
8
9
9
18
2
4
3
6
6
4
12
9
4
6
5
6
4.5
3
15
Answers
Start page
Similar shapes are shown in yellow
– were you right?
12
1
8
9
9
18
2
4
3
6
6
4
12
9
4
6
5
6
4.5
3
16
Start page
Scale factor = new value
old value.
Scale factor?
New value = 12 = 3 or 1.5
Old value
8 2 12cm
8cm
Scale factor?
5cm
New value = 8 = 2
Old value
12 3
7.5cm
Can you see the relationship between the two scale factors?
17
Start page
Using scale factor
Enlarge with scale
factor 3
a = 9 x 3 = 27cm
9cm
a
What will the scale
factor be?
b
SF = new/old = 9/27 = ⅓
OR reciprocal of 3 = ⅓
15cm
b = 15 x ⅓ = 15 ÷ 3 = 5cm
18
Similar shapes - summary
c
a
z
b
y
Ratio a:b:c = ratio x:y:z
So: a = x
a=x
b=y
x
b
y c z
c z
To see whether 2 shapes are similar, put each
ratio in its simplest form and see if they match.
Scale factor = new measurement
old measurement
Old measurement x SF = new measurement
new
SF
old
- Scale factor more than 1 => shape gets bigger
- Scale factor less than 1 => shape gets smaller
- Congruent shapes are similar shapes with SF = 1
Remember: only side lengths change; angles stay the same!
19
16.2 Triangles
p. 356
Introduction:
Quick Review
Objective: learn how to classify triangles and solve problems
involving angle measures of triangles
Vocabulary:
• acute triangle = contains only acute angles
• obtuse triangle = contains only one obtuse angle
• right triangle = contains only one right angle
• equilateral triangle = three congruent sides
• isosceles triangle = exactly two congruent sides
• scalene triangle = no congruent sides
Guided Learning:
http://www.mathwarehouse.com/geometry/triangles/interact
ive-triangle.htm
http://www.hbschool.com/glossary/math2/index6.html
http://jmathpage.com/JIMSGeometrypage.html
http://www.bbc.co.uk/schools/ks2bitesize/maths/shape_space/sh
apes/play.shtml
16.3 Find a Pattern
p. 360
Introduction:
Quick Review
Objective: learn how to use the strategy “find a pattern” to
solve problems
Vocabulary:
• regular polygon = polygon which all sides and angles are
congruent
http://www.hbschool.com/glossary/math2/index6.html
16.4 Quadrilaterals
p. 362
Introduction:
Quick Review
Objective: learn how to identify, classify, and compare
quadrilaterals
http://www.hbschool.com/glossary/math2/index6.html
http://jmathpage.com/JIMSGeometrypage.html
16.5 Draw Plane
Figures
p. 366
Introduction:
1. Quick Review
• Objective: learn how to draw plane geometric figures
Square Dot Geoboard
Square Dot Paper
Isometric Dot Geoboard
Isometric Dot Paper
16.6 Circles
p. 368
Introduction:
1. Quick Review: Complete on your white board
2. Objective: Learn how to identify and draw parts of circles
3. Warm-Up:
*Draw a dot on your white board, label it “O”. Next, draw a circle
around the center dot you just drew.
*Draw a radius and label it “radius” - someone explain how you did
it!
*Draw a diameter and label it “diameter” - someone explain how
you did it!
*Draw a chord and label it “chord” - someone explain how you did
it!
16.6 Circles
continued...
Vocabulary:
• radius - line segment with one endpoint at the center of a circle
and the other endpoint on the circle
• diameter - line segment passing through the center of a circle
and has both endpoints on the circle
• chord - line segment with its endpoints on a circle
Harcourt Math Glossary
Properties of Polygons
Name
polygon
isosceles triangle
scalene triangle
equilateral triangle
right triangle
parallellogram
rectangle
rhombus
square
trapezoid
Sometimes
Always
Never