I can calculate the motion of

heavenly bodies, but not the

madness of people.

c n e w t o nAASI

N I C E5 = 10 1 = x x = 10 2 = 10

2 x 3 6 4 8 3 x

S T O W A3 = x x = 3 4 = 2 1 = 2 1 = 3

4 16 12 6 6 x 4 x x 27

2 12 9 9 5 4 15 8 6 3 4

I can calculate the motion

of heavenly bodies, but not the madness of people.

Congruent Triangles

The same shape but different in size

Similar

Trianges

Similar Triangles

1. Class will be divided into three groups by color coding

2. Each group will be assign to draw a triangle with specific measurement in inches using a meterstick

a. Group1 will make ∆ABC with AB is the longest side

b. Group 2 will make ∆DEF with DE is the longest side

c. Group 3 will make ∆GHI with GH is the longest side

3. The group will assign their leader to measure each angles.

4. Make a proportion by sharing the work of each group

a. Group 1 will take the work of group 2

b. group 2 will take the work of group 3

c. group 3 will take the work of group 1

Then observe the relationship of their sides and angles

5. The group leader and the assistant leader will be the one to present their work.

D

A

C

B

E

F

G

H

I

∆

3018

24

2012

16

106

8

D

A

C

B

E

F

G

H

I

AB

DE=

AC

DF=

BC

EF

DE

GH= DF

GI=

EF

HIGH

AB= GI

AC=

HI

BC

∆ABC ~ ∆DEF ∆DEF ~ ∆GHI ∆GHI ~ ∆ABC

30 18

24

20 12

16

106

8

A

B

C90°

35°

90°35°

F

E

D90°35°

I

H

G

∆ABC ∆DEF ∆GHI

Measures of

Corresponding

Sides

AB =

BC =

AC =

DE =

EF =

DF =

GH =

HI =

GI =Measures of

Corresponding

Angles

m∠A =

m∠B=

m∠C =

m∠D =

M∠E =

m∠F =

m∠G =

m∠H =

m∠I =

30

18

24

20

12

16

10

6

8

35° 35° 35°

55° 55° 55°

90° 90° 90°

∆ABC ~ ∆DEF

∆DEF ~ ∆GHI

∆GHI ~ ∆ABC

1. Corresponding angles are

congruent (same measure)

2. Corresponding sides are all

in the same proportion

10

35° 60°

TU

V

Y

WX

35

8

16

6

TV

WY

UV

XY

510

5XY

5

=

=

3

XY

= 30

5

XY 6=

5

10

3

6

TV

WY

UV

XY

30=

=

=

30

∆TUV ~ ∆WXY

A B

C

D

F

= 3

Use FULL sides of the triangles, cross multiply and solve.

Here are the solutions letting BE = x.

8x= 36

x = 4.5

= 2.7mx

1, 2. 3.

4.5.

x

x

x

1. X = 12

2. X = 20

3. X = 12

4. X = 13.33

5. X = 17.5

1. Do Testyourself nos.

1-10 on page 152 of your textbook.

2. How to tell the triangles are similar?