Indirect Measurement and Additional Similarity Theorems 8.5.

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Presentation transcript:

Indirect Measurement and Additional Similarity Theorems 8.5

Learn the triangle angle bisector theorem. Learn the proportional altitudes theorem. Learn the proportional medians theorem. homework

Proportional Angle Bisectors Theorem homework

Proportional Altitudes Theorem homework

Proportional Medians Theorem homework

Proportional Angle Bisector Theorem Find PS and SR. 40(x – 2) = 32(x + 5) PS = x – 2 SR = x + 5 40x – 80 = 32x + 160 PS = 28 SR = 35 8x = 240 x = 30 homework

Proportional Altitudes Theorem The drawing of the table below has legs AE and CG. AC measures 12 inches and GE measures 36 inches. If BD measures 7 inches, what is the measure of DF and what is the height of the table? A B C D 12x = 252 x = 21 Therefore, DF = 21, and the table is 28 inches tall. homework

Proportional Medians Theorem In the figure, EFD ~ JKI. EG is a median of EFG and JL is a median of JKL. Find JL if EF = 36, EG = 18, and JK = 56. 36 18 56 E D G F K J I L x 1008 = 36x x = 28 Therefore, JL = 28. homework

Use indirect measure to find the missing value. homework

Use indirect measure to find the missing value. 10x = 360 x = 36 homework

Use indirect measure to find the missing value. x = 27 feet homework

Use indirect measure to find the missing value. 4x = 55 x = 13.75 feet homework

Use the Triangle Angle Bisector Theorem find ST and SR 7.5x + 37.5 = 12.5x – 62.5 –5x = –100 x = 20 SR = 25, ST = 15 homework 13

EXAMPLE 4 In the diagram, QPR  RPS. Use the given side lengths to find the length of RS . 7x = 195 – 13x x = 9.75 homework

Use the Triangle Angle Bisector Theorem find x. 42x2 = 50x2 – 20x 8x2 – 20x = 0 4x(2x – 5) = 0 x = 0 or x = 2.5 homework

Use the Triangle Angle Bisector Theorem find x. 4x = 36 – 6x 10x = 36 x = 3.6 homework

Assignment 8.5 Indirect Measurment