Mrs. McConaughy Geometry 1

Proportional Parts/Areas/Volumes

During this lesson, you will: Determine measures of corresponding parts of similar triangles Determine ratios of areas in similar polygons (or circles) Determine ratios of volumes in similar polygons (or circles)

Mrs. McConaughy Geometry 2

PART 1: Corresponding Parts of Similar Triangles

VOCABULARY REVIEWBefore we start, sketch and label the indicated part in each triangle below:

Angle bisector 0X O

B S

Median BM B

O

E

Altitude AH A

M T

X MH

Mrs. McConaughy Geometry 3

Proportional Parts Theorem

Proportional Parts Theorem: If two triangles are similar, then the corresponding ________, _________, and _____________ are __________to the corresponding sides.

altitudesmediansangle bisectors

proportional

Mrs. McConaughy Geometry 4

EXAMPLE: CA = AP = CP = CL

DA AY DY DF

35 = AP = CP = 25

21 AY DY DF

5 = AP = CP = 25

3 AY DY DF15

Mrs. McConaughy Geometry 5

Part 2: Proportions with Area

Proportional Area Theorem: If two polygons (or circles) have corresponding sides (or radii) in the ration of m/n, then their areas are in the ratio of ______.m2/n2

Mrs. McConaughy Geometry 6

EXAMPLES:

The ratio of the areas of two similar triangles is in the ratio of 4:9. What is the ratio of their altitudes?

The ratio of the medians of two similar triangles is 4:5. What is the ratio of their areas?

Mrs. McConaughy Geometry 7

Part 3: Proportions with Volume

Proportional Volume Theorem: If two similar solids have corresponding dimensions in the ratio of m/n, then their volumes are in the ratio of ______.

m3/n3

Mrs. McConaughy Geometry 8

EXAMPLES:

The surface areas of two cubes are in the ratio of 25: 64. What is the ratio of their volumes?

The ratio of the weights of two spherical steel balls is 27:64. What is the ratio of the diameters of the steel balls?

Mrs. McConaughy Geometry 9

HOMEWORK ASSIGNMENT:

Day 1: Proportional Parts WS

Day 2: Proportional Area WS

Day 3: Proportional Volume WS