Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will: Determine...

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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)

Transcript of Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will: Determine...

Page 1: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

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)

Page 2: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

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

Page 3: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

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

Page 4: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

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

Page 5: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

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

Page 6: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

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?

Page 7: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

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

Page 8: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

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?

Page 9: Mrs. McConaughyGeometry1 Proportional Parts/Areas/Volumes During this lesson, you will:  Determine measures of corresponding parts of similar triangles.

Mrs. McConaughy Geometry 9

HOMEWORK ASSIGNMENT:

Day 1: Proportional Parts WS

Day 2: Proportional Area WS

Day 3: Proportional Volume WS