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8.5 Three Theorems Involving Proportion

Study and apply three essential theorems in establishing proportionality in geometry. Understand the Side-Splitter Theorem, Parallel Lines Theorem, and Angle Bisector Theorem through practical examples and proofs. Enhance your geometry skills with this comprehensive lesson.

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8.5 Three Theorems Involving Proportion

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  1. 8.5 Three Theorems Involving Proportion Objective: After studying this section, you will be able to apply three theorems frequently used to establish proportionality.

  2. 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: D C

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

  4. 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)

  5. Given: A 1 2 Prove: B D C

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

  7. Given: a ll b ll c ll d lengths as shown KP = 24 Find: KM K F a 5 M b G 2 H O c 8 J P d

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

  9. Given: W Conclusion: A X Z Y

  10. Given: C D H B E Prove: F G

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

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