Transcript x - Mags Maths

Similar Figures
Enlargement
If 2 angles in the triangle are the same,
the third angle must also match and so
we have a similar figure.
The sides will be in proportion to one
another.
10
8
4
5
3
6
Sometimes the triangles sit
inside one another
A
D
C
B
E
Both triangles ABC and DEC have a right angle
and both have the same angle C
A
D
C
B
E
We can now look at the ratios.
A
D
9
4
C
B
E
7
x
Separate the triangles.
A
D
4
9
x
E
C
B
7
C
Ratios of sides:
x 4
=
7 9
A
D
4
9
x
E
C
B
7
C
The triangles could be
oriented differently
A
D
12
x
C
B
6
E
8
The triangles could be
oriented differently
A
B and D are both right
angles.
D
C is common to both
triangles
So A must be the
same as E
C
B
E
The triangles could be
oriented differently
A
D
12
x
C
B
6
E
8
Re-draw the triangles
matching angles
A
E
C
D
B
C
A
D
12
x
B
A
E
C
6 E
8 E
8
x
12
D
C
C
B
14
We need to find length AC first using Pythagoras’
A
E
8
x
12
D
C
C
B
14
We need to find length AC first using Pythagoras’
AC2 = 122 + 142
AC = 18.439...
A
E
8
x
12
D
C
C
B
14
We need to find length AC first using Pythagoras’
AC2 = 122 + 142
AC = 18.439...
A
E
18.439…
8
x
12
D
C
C
B
14
Now we can use ratios to find x
8
x
=
18.439... 12
8 ´12
Þx=
= 5.2
18.439
A
E
18.439…
8
x
12
D
C
C
B
14
Different orientation again
A
B
AB//CD
E
C
D
Because AB//CD, A=D and B=C.
This means the triangles are similar.
9.85
A
B
y
11.2
AB//CD
E
16.37
7.45
D
C
x
Re-draw the triangles
9.85
A
B
y
11.2
E
16.3
7
D
7.45
C
x
9.85
A
y
B
11.2
E
Match angles
9.85
A
B
y
11.2
9.85
A
y
11.2
E
16.3
7
D
7.45
C
x
B
E
x
D
C
7.45
16.3
E
Match angles
Using ratios
7.45
x
=
11.2 9.85
7.45 ´ 9.85
x=
= 6.55
11.2
9.85
A
y
B
11.2
E
x
D
C
7.45
16.3
E
Match angles
Using ratios
7.45
x
=
11.2 9.85
7.45 ´ 9.85
x=
= 6.55
11.2
11.2
y
=
7.45 16.3
11.2 ´16.3
y=
= 24.5
7.45
9.85
A
y
B
11.2
E
x
D
C
7.45
16.3
E