Mrs. McConaughyGeometry1 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. McConaughyGeometry2 PART 1: Corresponding Parts of Similar Triangles VOCABULARY REVIEW Before 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 XM H

Mrs. McConaughyGeometry3 Proportional Parts Theorem Proportional Parts Theorem: If two triangles are similar, then the corresponding ________, _________, and _____________ are __________to the corresponding sides.

Mrs. McConaughyGeometry4 EXAMPLE: CA = AP = CP = CL DA AY DY DF 35 = AP = CP = AY DY DF 5 = AP = CP = 25 3 AY DY DF

Mrs. McConaughyGeometry5 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 ______.

Mrs. McConaughyGeometry6 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. McConaughyGeometry7 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 ______.

Mrs. McConaughyGeometry8 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. McConaughyGeometry9 HOMEWORK ASSIGNMENT: Day 1: Proportional Parts WS Day 2: Proportional Area WS Day 3: Proportional Volume WS