8.5 Three Theorems Involving Proportion

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Presentation transcript:

8.5 Three Theorems Involving Proportion Objective: After studying this section, you will be able to apply three theorems frequently used to establish proportionality.

(Side-Splitter Theorem) Theorem If a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally. (Side-Splitter Theorem) A Given: BE ll CD E B Prove: C D

Theorem. If three or more parallel lines are Theorem If three or more parallel lines are intersected by two transversals, the parallel lines divide the transversals proportionally. A B Given: AB ll CD ll EF C G Prove: D E F

Theorem. If a ray bisects an angle of a Theorem If a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides. (Angle Bisector Theorem)

Given: A 1 2 Prove: B D C

Given: BE ll CD lengths as shown A 7 4 6 Find: a. ED b. CD E B 2 C D

Given: a ll b ll c ll d lengths as shown KP = 24 Find: KM F K a 5 M b 8 J P d

V Given: lengths as shown 8 10 Find: ST R 4 S x T

Given: W Conclusion: A X Y Z

Given: C D H B E Prove: F G

Summary: In your own words, state how you can apply the three theorems learned in this lesson. Homework: worksheet