Congruent and similar shapes

1
Congruent and similar shapes
Congruent shapes
Similar shapes
2
Congruent shapes
3
1. Which of these shapes are congruent to the
yellow one?
Start page
4
1
3
2
5
7
8
6
Answers
Hints
4
Congruent shapes are all shown in yellow were
you right?
Start page
4
1
3
2
5
7
8
6
5
What makes a pair of shapes congruent?
Start page

• 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
6
2. Which of these shapes are congruent to the
yellow one?
Start page
1
4
2
3
8
5
6
9
7
Answers
7
Congruent shapes are all shown in yellow were
you right?
Start page
1
2
5
8
Similar shapes
9
Which of these shapes are similar to the yellow
one?
Start page
4
1
3
2
5
7
8
6
Answers
Hints
10
Similar shapes are all shown in yellow were you
right?
Start page
1
4
3
2
5
7
8
6
11
What makes a pair of shapes similar?
Start page

• 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 doesnt change ? congruent
  too
• Click the green box if you want to go back to the
  similar shapes question page.

Question page
12
Using similarity
Start page
Since shapes are similar, their sides are in the
same proportion
gt 6 a 9 12
9cm
12cm
Multiply both sides by 12 gt 12 x 6 a
9
6cm
gt a 12 x 2 4 x 2 3 1
a
gt a 8cm
13
Which of these shapes are similar to the yellow
one?(They arent drawn to scale)
Start page
1
2
12
3
8
9
9
18
4
4
5
6
6
6
12
9
4.5
4
3
6
Answers
14
Similar shapes are shown in yellow were you
right?
Start page
9
6
15
Scale factor new value old value.
Start page
New value Old value
12 3 or 1.5 8 2
8cm
12cm
5cm
New value Old value
8 2 12 3
7.5cm
Can you see the relationship between the two
scale factors?
16
Using scale factor
Start page
Enlarge with scale factor 3
a 9 x 3 27cm
9cm
a
What will the scale factor be?
b
SF new/old 9/27 ?
OR reciprocal of 3 ?
15cm
b 15 x ? 15 3 5cm
17
Similar shapes - summary
Ratio abc ratio xyz
So a x a x b y 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

• - Scale factor more than 1 gt shape gets bigger
• Scale factor less than 1 gt shape gets smaller
• Congruent shapes are similar shapes with SF 1

Remember only side lengths change angles stay
the same!