similar triangles have the same angles

Similar triangles don’t just look the same

Similarity is a key piece of geometry jargon. If two shapes are similar, then

they don’t just look alike, one is an exact scaled version of the other. This

means that they have the same (equal) angles.

T

hese tr

iangles ar

e simil

ar. In

geometry terms, w

e don’t just

mean they kinda look the same.

Simil

ar triangles

don’t have t

o be

the same w

ay up.

86°

53°

41°

86°

53°

41°

41°

53°

86°

But don’t take our word for it…check that it all adds up:

Tick marks to show that

our line is parallel

86

o

41

o

53

o

41

o

53

o

86

o

1

Take a big triangle, and draw

Line part way up

the triangle

a line part way up the triangle,

parallel with the base.

2

This creates a mini triangle

which shares the angle at the

peak of the big triangle.

58 Chapter 2

similarity and congruence

Using what you know about parallel lines and the F pattern, find the two

mystery angles to complete the mini triangle you’ve created.

If the line is drawn parallel to one of the other sides, do you still end up with the

same angles in your mini triangle?

Remember the F

, N, Z pa

tterns

f

rom chapter 1? No? C

heck out

page 40.

?

?

86

o

41

o

53

o

?

?

41

o

86

o

53

o

41

o

86

o

53

o

?

?

you are here 4 59

the F pattern in action

Using what you know about parallel lines and the F pattern, find the two

mystery angles to complete the mini triangle you’ve created.

If the line is drawn parallel to one of the other sides, do you still end up with the

same angles in your mini triangle?

T

his F pa

ttern is

upside down and

back t

o f

ront!

The F pa

ttern

is upside down.

41

o

53

o

41

o

53

o

The angles always come out the same—it doesn’t matter which side the line is parallel to:

86

o

53

o

86

o

53

o

41

o

41

o

86

o

41

o

86

o

86

o

41

o

53

o

41

o

53

o

41

o

86

o

53

o

53

o

86

o

41

o

86

o

53

o

86

o

41

o

60 Chapter 2

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