Applications of Similarity

Use ratios and corresponding parts in applications of similarity.

Lesson 5 of 53 parts Practice Flashcards

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Indirect Measurement

Objective: Solve problems involving indirect measurement.

Similar triangles allow indirect measurement with proportional corresponding sides.

Worked examples

Try itA 4-unit stick casts a shadow 8 units long. At the same time a tree casts a 16-unit shadow. Find tree height.Show answer

8. The stick shadow is twice its height; the tree shadow is twice the tree height too.

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Objective: Solve problems involving indirect measurement.

Similar triangles allow indirect measurement with proportional corresponding sides.

Worked examples

Try itA 4-unit stick casts a shadow 8 units long. At the same time a tree casts a 16-unit shadow. Find tree height.Show answer

8. The stick shadow is twice its height; the tree shadow is twice the tree height too.

Objective: Solve problems involving scale drawings.

A scale drawing multiplies each real length by one consistent scale factor.

Worked examples

Try itOn a scale drawing, 1 cm represents 3 m. How many meters does 3 cm represent?Show answer

9. Multiply 3 cm by the scale of (i+2) m per cm.

Objective: Solve problems involving similar right triangles.

The altitude to the hypotenuse of a right triangle creates triangles similar to the original and to each other.

Worked examples

Try itAn altitude to the hypotenuse splits it into segments of lengths 3 and 7. What is the full hypotenuse length?Show answer

10. The whole hypotenuse is the sum of its two parts.

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