Similar Polygons.

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Concept: Use Similar Polygons

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Presentation transcript:

Similar Polygons

Similar Polygons Similar (~) – Figures are similar when they have the same shape but may be different in size. Their corresponding angles are congruent and the lengths of their corresponding segments are proportional. Vertices in similar figures must be listed in corresponding order, just like for congruent figures. Scale factor – The scale factor, or magnitude of dilation, is the ratio of the corresponding lengths of similar figures.

Determine whether the pair of figures is similar. Justify your answer Determine whether the pair of figures is similar. Justify your answer. a. Example 2-1e

The ratio of the measures of the corresponding sides are equal and the corresponding angles are congruent, Answer: Both triangles are isosceles with base angles measuring 76º and vertex angles measuring 28º. Example 2-1e

Determine whether the pair of figures is similar. Justify your answer. b. Determine whether the pair of figures is similar. Justify your answer. Answer: Only one pair of angles are congruent, so the triangles are not similar. Example 2-1f

A space shuttle is about 122 feet in length A space shuttle is about 122 feet in length. The Science Club plans to make a model of the space shuttle with a length of 24 inches. What is the scale factor of the model compared to the real space shuttle? Answer: Example 2-2c

The two polygons are similar. a. Write a similarity statement. Then find a, b, and ZO. b. Find the scale factor of polygon TRAP to polygon . Answer: ; Answer: Example 2-3g

Quadrilateral GCDE is similar to quadrilateral JKLM with a scale factor of If two of the sides of GCDE measure 7 inches and 14 inches, what are the lengths of the corresponding sides of JKLM? Answer: 5 in., 10 in. Example 2-4c

An historic train ride is planned between two landmarks on the Lewis and Clark Trail. The scale on a map that includes the two landmarks is 3 centimeters = 125 miles. The distance between the two landmarks on the map is 1.5 centimeters. If the train travels at an average rate of 50 miles per hour, how long will the trip between the landmarks take? Answer: 1.25 hours Example 2-5d