Similar is a mathematical word meaning the same Similar is a mathematical word meaning the same shape.shape.

We say that two triangles , triangle FDE and We say that two triangles , triangle FDE and triangle LMK, are similar if the ratio of each side is triangle LMK, are similar if the ratio of each side is similar.similar.

FD : DE : EF = LM : MK : KLFD : DE : EF = LM : MK : KL

This equation of two three term ratios can also be This equation of two three term ratios can also be written in fraction form:written in fraction form:

FDLM

DEMK

EFKL= = Corresponding sides are equalCorresponding sides are equal

NOTE:

All sides of one triangle must be either all in the numerator or denominator.

In similar triangles, corresponding angles are In similar triangles, corresponding angles are equal.equal.

F = F = L L

D = D = M M

E = E = K K

IMPORTANT:IMPORTANT:

If you know two triangles are If you know two triangles are similarsimilar, then their , then their corresponding angles are equalcorresponding angles are equal..

ConverselyConversely, if two triangles have equal , if two triangles have equal corresponding angles, then the triangles are corresponding angles, then the triangles are similar.similar.

Prove the two triangles are similar?Prove the two triangles are similar?

SOLUTION:SOLUTION:

Angles:Angles:

K = A

L = B

M = C

Sides:Sides:

KLAB

KMAC

LMBC

= =

812

1015

69

= =

10801620

10801620

10801620

= =

Since corresponding angles are equal, then corresponding sides are equal. Therefore the two triangles are similar.

Prove the two triangles are similar?Prove the two triangles are similar?

SOLUTION:SOLUTION:

Angles:Angles: Sides:Sides:

Prove the two triangles are similar?Prove the two triangles are similar?

SOLUTION:SOLUTION:

Angles:Angles:

L = K

M = S

O = T

Sides:Sides:

LMKS

LOKT

MOST

= =

45

56.25

67.5

= =

187.5234.38

187.5234.38

187.5234.38

= =

Since corresponding angles are equal, then corresponding sides are equal. Therefore the two triangles are similar.

Solve for the unknown values.Solve for the unknown values.

SOLUTION:SOLUTION: Sides:Sides:

ABDE

BCDC

ACEC

= =

x12

39

4y

= =

Angles:Angles:

A= E

B = D

C= C

39

4y

= x12

=39

9(4) = 3y9(4) = 3y

36 = 3y36 = 3y

12 = y12 = y

3(12) = 9x3(12) = 9x

36 = 9x36 = 9x

4 = x4 = x

Solve for the unknown values.Solve for the unknown values.

SOLUTION:SOLUTION: Sides:Sides:

Angles:Angles:

Solve for the unknown values.Solve for the unknown values.

SOLUTION:SOLUTION: Sides:Sides:

CTPR

TZRZ

CZPZ

= =

x12

69

3y

= =

Angles:Angles:

C= P

T = R

Z= Z

69

3y

= x12

=69

9(3) = 6y9(3) = 6y

27 = 6y27 = 6y

4.5 = y4.5 = y

6(12) = 9x6(12) = 9x

72 = 9x72 = 9x

8 = x8 = x

Class work

• Copy down examples

• Finish Lesson 18(2) worksheet.