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Chapter 2

Investigating Geometric Figures

2-6 Congruent and Similar Figures

Objective: Measure congruent and similar figures; Using properties of congruence and similarity

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HW Solutions Practice 2-5

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Solving proportions

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Marta is making a scale drawing of her bedroom. Her rectangular room is 12 feet wide and 15 feet long. On the scale drawing, the width of her room is 5

inches. What is the length?

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Congruent Figures

-- have exactly the same size and shape

** When 2 figures are congruent you can slide, flip, or turn one so that it fits exactly on the other one.

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Congruent Circles

-- have congruent radii

G HR

S

If GR = 9,

then HS = ____

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Congruent polygons

--have congruent corresponding parts

The matching angles and sides of congruent polygons are called corresponding parts.

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Matching vertices are called

corresponding vertices.

When you name congruent polygons, always list corresponding vertices in the same order.

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J

K

L

OM

N

JKL = MNOList the congruent corresponding parts.

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Similar Polygons

-- two figures that have the same shape but not necessarily the same size

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Two polygons are similar if:

-- corresponding angles are =

AND

-- corresponding sides are proportional

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Describing Similar Polygons

Identify the pairs of congruent angles and corresponding sides.

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Identifying Similar PolygonsDetermine whether the polygons are similar. If so, write the similarity ratio

and a similarity statement.

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Identifying Similar Polygons

Determine whether the polygons are

similar. If so, write the similarity ratio and a similarity statement.

72°56°

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Check It Out! Determine if ∆JLM ~ ∆NPS. If so, write the similarity ratio and a similarity statement.

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Hobby Application

Find the length of the model to the nearest tenth of a centimeter.

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Check It Out!

A boxcar has the dimensions shown. A model of the boxcar is 1.25 in. wide. Find the length of the model to the

nearest inch.

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HW # 30p. 105 # 2-28, 35-37,40-42

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