6.5 Parts of Similar Triangles

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Presentation transcript:

6.5 Parts of Similar Triangles

Objectives Recognize and use proportional relationships of corresponding perimeters of similar triangles Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles

Proportional Perimeters Theorem If two Δs are similar, then the perimeters are proportional to the measures of the corresponding sides.

Example 1: C If and find the perimeter of Let x represent the perimeter of The perimeter of

Example 1: Proportional Perimeter Theorem Substitution Cross products Multiply. Divide each side by 16. Answer: The perimeter of

Your Turn: If and RX = 20, find the perimeter of R Answer:

Special Segments of ~ Δs Theorem 6.8 In ~ Δs, corresponding altitudes are proportional to the measures of the corresponding sides Theorem 6.9 In ~ Δs, corresponding angle bisectors are proportional to the measures of the corresponding sides Theorem 6.10 In~ Δs, corresponding medians are proportional to the measures of the corresponding sides

Example 2: In the figure, is an altitude of and is an altitude of Find x if and K

Example 2: Write a proportion. Cross products Divide each side by 36. Answer: Thus, JI = 28.

Your Turn: In the figure, is an altitude of and is an altitude of Find x if and N Answer: 17.5

Example 3: The drawing below illustrates two poles supported by wires. , , and Find the height of the pole .

Example 3: are medians of since and If two triangles are similar, then the measures of the corresponding medians are proportional to the measures of the corresponding sides. This leads to the proportion measures 40 ft. Also, since both measure 20 ft. Therefore,

Example 3: Write a proportion. Cross products Simplify. Divide each side by 80. Answer: The height of the pole is 15 feet.

Your Turn: The drawing below illustrates the legs, of a table. The top of the legs are fastened so that AC measures 12 inches while the bottom of the legs open such that GE measures 36 inches. If BD measures 7 inches, what is the height h of the table? Answer: 28 in.

Assignment Geometry Pg. 320 #10 – 24 Pre-AP Geometry Pg. 320 #10 – 26 evens, 33, 34, 36