Wednesday, September 25th

S is the centroid. 1. If MS=12, what is SP?2. If NQ=18, what is SQ?

Warm Up

Identify similar polygons.

Apply properties of similar polygons to solve problems.

Today’s Goal

Which shapes are similar and how do you know?

1.

2. 3.

Figures that are similar (~) have the same shape but not necessarily the

same size.

Remember-Congruent

Have the same size

and shape

EXACTALY THE

SAME!!!!!

Represented by:

Two polygons are similar polygons if and only if their corresponding angles are congruent and their corresponding side lengths are proportional.

Definition

Similar FiguresTwo figures are similar if• the measures of the corresponding angles are equal• the ratios of the lengths of the corresponding sides are proportional

Similar figures have the same shape but not necessarily the same size.

Finding missing angles

• Hint: Remember angles are the same in corresponding angles!

What is angle D? <D

#1 Identify the pairs of congruent angles and corresponding sides

N Q and P R. By the Third Angles Theorem, M T.

0.5

B G and C H. By the Third Angles Theorem, A J.

#2 Identify the pairs of congruent angles and corresponding sides

A similarity ratio is the ratio of the lengths of

the corresponding sides of two similar polygons.

The similarity ratio of ∆ABC to ∆DEF is , or .

The similarity ratio of ∆DEF to ∆ABC is , or 2.

Think: What am I multiplying or dividing all sides by to get

the lengths of the other triangle?

Also known as the SCALE FACTOR or DIALATION

Writing a similarity statement is like writing a congruence statement—be sure to list corresponding vertices in the same order.

Writing Math

#1 Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.

∆ABCD and ∆EFGH

Step 1 Identify pairs of congruent angles.

P R and S W isos. ∆

Step 2 Compare corresponding angles.

Since no pairs of angles are congruent, the triangles are not similar.

mW = mS = 62°

mT = 180° – 2(62°) = 56°

Step 1 Identify pairs of congruent angles.

#2 Determine if ∆JLM ~ ∆NPS. If so, write the similarity ratio and a similarity statement.

N M, L P, S J

Step 2 Compare corresponding sides.

Thus the similarity ratio is , and ∆LMJ ~ ∆PNS.

Finding Scale Factor Practice

Ticket to Go: Textbook page 249

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