P.O.D. Use your knowledge of proportions to solve for x = x 24 3  24 = 8  x 72 = 8x ÷8 9 = x Use your knowledge of proportions to solve for t = t 8.5  t = 3  t = ÷8.5÷8.5 t = 4.5

P.O.D. # basic advanced Find the values of x and y. Find the values of x = 3 x 3  8 = 5  x 24 = 5x ÷5 4.8 = x 3838 = 2 y 3  y = 8  2 3y = 16 ÷3 y = = x 4 8  x = 3  4 8x = 12 ÷8 x = 1.5

4-5 Similar Figures Objective: To use proportions to find missing lengths in similar figures

A polygon is a closed plane figure formed by three or more line segments that do not cross

Two polygons are similar polygons if Corresponding angles have the same measure, and The lengths of the corresponding sides form equivalent ratios Two polygons are similar polygons if Corresponding angles have the same measure, and The lengths of the corresponding sides form equivalent ratios

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 = = = 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.

Example: I do 4 6 x = 4x4x 6  x = 4  9 6x = 36 ÷6 ÷6 x = 6 AB C D L M N O

Whiteboard: Which side on the larger triangle corresponds to the green side of the smaller triangle?

Whiteboard Time: We do 4 6 x 9 AB C D L M N O Which angle corresponds to Angle L? Angle A

2 3 9 x 3232 = 9x9x 3  x = 2  9 3x = 18 ÷3 ÷3 x = 6 Whiteboard:

63 42 = x 60 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:

Now let’s try some on our own: Pg #2-18 even

Whiteboard: ≠