P.O.D. #4basic advancedUse your knowledge of proportions to solve for x.

38

= x24

3 24 = 8 x72 = 8x÷8 ÷8 9 = x

Use your knowledge of proportions to solve for t.

8.5 3 = 12.75

t

8.5 t = 3 12.75 8.5t = 38.25 ÷8.5 ÷8.5 t = 4.5

Similar & Congruent Figures

Figures that have the same shape but not necessarily the same size are called similar figures.

When two figures are similar, their corresponding sides are in proportion.

4

3

5

8

6

10

48

36

510

=

=

=

12

12

12

This means the ratios of the lengths of the corresponding sides are equal.

The corresponding angles of similar figures are congruent.

This means the corresponding angles have the same measure.

30°

60°90°

30°

60°90°

Figures that have the same shape AND size are called congruent figures.

When two figures are congruent, the corresponding sides are congruent AND the corresponding angles are congruent.

Whiteboard:

6

9

6

9

Whiteboard:

1

1

4

3

11

43≠

Whiteboard:

23

9 x

32

= 9x

3x = 29 3x = 18 ÷3 ÷3 x = 6

Whiteboard:

6342

= x60

Old Faithful in Yellowstone National Park shoots water 60 feet into the air that casts a shadow of 42 feet. What is the height of a nearby tree that casts a shadow 63 feet long? Assume the triangles are similar.

63 60 = 42 x 3780 = 42x ÷42 ÷42 90 = x

Whiteboard: