Do Now 1/6/14 Copy HW in your planner. Text p. 166, #1-19 all, 23 &24 In your notebook, use cross products to tell whether the ratios below are proportional (equal). 16 6 , 40 15 3 8 18 46 8 9 , , 24 27 28 12 , 42 18 240 = 240; equal 138 = 144; not equal 216 = 216; equal 504 = 504; equal

“Basic Geometry Concepts” Point position in space represented by a dot. L A D Z K

Plane a flat surface that extends on forever in all directions. How many planes on this figure?

Line segment part of a line with 2 endpoints and all the points in between. D E C F

Line a straight path extending without end in 2 directions. R S T

Ray Part of a line that begins at a point and extends in one direction without ending. B K A J AB K JK A

Congruent Two line segments are congruent when they are the same length. C D E F 3

Angle Two rays that begin at the same point. D Sides C Vertex E

Naming Angles The following angle can be named in three ways: B C A Vertex

Objective SWBAT use ratios to determine if two figures are similar

Section 4.4 “Similar Figures” Two figures are SIMILAR FIGURES if they have the same shape but not necessarily the same size. The symbol ~ indicates two figures are similar. Two figures are similar if: 1). The measures of their corresponding angles are equal 2). The ratios of the lengths of their corresponding sides are proportional (equal ratios)

Corresponding angles – matching angles of two figures When 2 angles have the same measure, they are marked with the same symbol or measurement. D 35° A 35° 25° 120° F E 25° C 120° B

Corresponding sides – matching sides of two figures D A F E C B

Given ABC ~ XYZ, name the corresponding angles and corresponding sides.

Identify the corresponding sides in the pair of triangles Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E AB corresponds to DE. 16 in 10 in A C 28 in BC corresponds to EF. 4 in D 7 in 40 in F AC corresponds to DF. B AB DE = ? BC EF = ? AC DF Write ratios using the corresponding sides. 4 16 = ? 7 28 = ? 10 40 Substitute the length of the sides. 1 4 = ? 1 4 = ? 1 4 Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the triangles are similar.

Identify the corresponding sides in the pair of triangles Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether the triangles are similar. E AB corresponds to DE. 9 in 8 in A C 21 in BC corresponds to EF. 3 in D 7 in 32 in F AC corresponds to DF. B AB DE = ? BC EF = ? AC DF Write ratios using the corresponding sides. 3 9 = ? 7 21 = ? 8 32 Substitute the length of the sides. 1 3 = ? 1 3 = ? 1 4 Simplify each ratio. Since the ratios of the corresponding sides are not equivalent, the triangles are not similar.

With triangles, if the corresponding side lengths are all proportional, then the corresponding angles MUST have equal measures. With figures that have 4 or more sides, if the corresponding side lengths are all proportional, then corresponding angles MAY or MAY NOT have equal measures. ABCD is not similar to WXYZ because corresponding sides are proportional and but corresponding angles are NOT equal. QRST ~ ABCD because corresponding sides are proportional and corresponding angles are equal.

Tell whether the figures are similar. The corresponding angles of the figures have equal measure. MN QR = ? NO RS OP ST MP QT Write ratios using corresponding sides. 6 9 = ? 8 12 4 10 15 Substitute the length of the sides. 2 3 = ? Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.

Tell whether the figures are similar. 80° 90° 125° 65° M P N O 400 m 320 m 190 m 240 m Q T R S Tell whether the figures are similar. 100 m 80 m 60 m 47.5 m 80° 90° 125° 65° M P N O 400 m 320 m 190 m 240 m Q T R S The corresponding angles of the figures have equal measure. MN QR = ? NO RS OP ST MP QT Write ratios using corresponding sides. Write ratios using corresponding sides. 60 240 = ? 80 320 47.5 190 100 400 Substitute the length of the sides. 1 4 = ? Simplify each ratio. Since the ratios of the corresponding sides are equivalent, the figures are similar.

Try it out Tell whether the figures are similar. 119° 55° 107° 79° 80° 135° 38° 59° 35° 86° NP QS = ? NO QR = ? PO RS Not similar; corresponding angles do not have equal measures Similar 7 14 = ? 4 8 = ? 6 12 1 2 = ? 1 2 = ? 1 2