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Lesson 2 Similar Polygons

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Last updated 4 months ago
27 Nsɛmmisa

Review of Lesson 1 - Ratios and Proportions

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Since corresponding sides of similar polygons are proportional, this means their side ratios are EQUAL.

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More Problems

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Solved solution for Question #27.

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Solve for x.

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Solve for x.

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Solve for x.

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Solve for x.

Lesson 2 - Similar Polygons

Key Objectives:

  1. Define similar polygons. Identify the attributes of similar polygons. Identify whether two polygons are similar

  2. Write a similarity statement

  3. Find missing angle measures of similar polygons

  4. Determine the scale factor (ratio of corresponding sides / ratio of similitude) between two similar polygons

  5. Use scale factor to find missing side lengths (angle bisectors/medians/altitudes) and perimeter of similar polygons

WHAT SIMILAR LOOKS LIKE / WHAT DOES IT MEAN FOR TWO POLYONS/FIGURES TO BE SIMILAR

These two triangles are SIMILAR

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How are the two triangles the SAME?

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How are the two triangles DIFFERENT?

Similar polygons have the SAME SHAPE but NOT (necessarily) the same SIZE.

You can abbreviate "similar to" by using the similar

symbol (

).

You write a similarity statement with corresponding vertices in order (just like a congruency statement).

--> read as "Triangle ABC is similar to Triangle DEF

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Mmuae Afoforo a Wobɛpaw:

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This video is a review of all topics covered up until this point. Watch the video if you need some extra calrification before attempting the below problems.

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What is the scale factor of Pentagon ABCDE to Pentagon RSTUV?

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If BC = 15, find ST. (Write the proportion in the show your work area)

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Find the scale factor between ABCD and RSTV?

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Find y.

The ratio of the perimeters (and altitudes/medians/angle bisectors) of similar polygons is EQUAL to the SCALE FACTOR / RATIO OF CORRESPONDING SIDES.

RATIO OF PERIMETERS = SCALE FACTOR

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In similar pentagons ABCDE and RSTUV, the perimeter of ABCDE is 60 inches. Find the perimeter of RSTUV.

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How to determine whether two polygons are similar?

  1. Make sure ALL pairs of corresponding angles are CONGRUENT

AND

  1. Find all of the side ratios to determine all side ratios are EQUAL.

If BOTH conditions are satisfied, then the polygons are SIMILAR.

(If only one or none of the conditions are met, the. polygons are NOT SIMILAR)

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Are the polygons similar? If they are, write a similarity statement and give the scale factor.

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Are the polygons similar? If they are, write a similarity statement and give the scale factor.

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USING SIMILAR POLYGONS TO FIND MISSING SIDES/ PERIMETERS AND ANGLE MEASURES

TO FIND A MISSING SIDE OF A SIMILAR POLYGON

  1. Find the scale factor of the similar polygon by using a pair of given corresponding side lengths.

  2. Write / solve a proportion setting the scale factor equal to the ratio of the missing side to its corresponding side (given)

TO FIND A MISSING ANGLE OF A SIMILAR POLYGON

  1. Set corresponding angles equal to each other.

  2. Sometimes have to use triangle angle sum theorem

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If ABCD

EFGD, find the value of y.

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Are the polygons similar? If they are, write the similarity statement and give the scale factor.

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What is the value of x?

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If Quadrilateral ABCD

Quadrilateral WXYZ , then what is the scale factor between the two similar polygons?

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