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)
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
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