Proportional Segments

Use ratios and corresponding parts in proportional segments.

Lesson 4 of 53 parts Practice Flashcards

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Triangle Proportionality

Objective: Solve problems involving triangle proportionality.

A line parallel to one side of a triangle divides the other two proportionally.

Worked examples

Try itA line parallel to a triangle side divides one other side into 4 and 7, and the corresponding first part of the second side is 8. Find its second part.Show answer

14. The corresponding parts have common ratio 2, so double the second part.

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Triangle Proportionality

Objective: Solve problems involving triangle proportionality.

A line parallel to one side of a triangle divides the other two proportionally.

Worked examples

Try itA line parallel to a triangle side divides one other side into 4 and 7, and the corresponding first part of the second side is 8. Find its second part.Show answer

14. The corresponding parts have common ratio 2, so double the second part.

Parallel-Line Partitions

Objective: Solve problems involving parallel-line partitions.

Parallel lines crossing transversals create proportional corresponding segments.

Three parallel lines cross two transversals, cutting segments 2 and 3 on one and 4 and 6 on the other.

Worked examples

Try itParallel lines cut two transversals with corresponding intervals 5 and 10. What is their length ratio first:second?Show answer

1:2. Each second interval is twice the first.

Solving Proportions

Objective: Solve problems involving solving proportions.

To solve a proportion, cross-multiply only after matching corresponding parts.

Worked examples

Try itSolve x/4 = 2/3 for x.Show answer

2.66667. Multiply both sides by the denominator to get x = 2(i+3)/3.

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