Similarity in Triangles Unit 13 Notes Definition of Similarity

Warm Up

Similarity in Triangles

Unit 13 Notes

Definition of Similarity

What does it mean to be Similar?

Similarity Definition• Two polygons are similar polygons if corresponding

angles are congruent and corresponding side lengths are proportional.

This is called the Similarity Ratio.

Ex.1 Use similarity statements.

Vocabulary: Similarity RatioIf two polygons are similar, then the ratio of the

lengths of two corresponding sides is called the Similarity Ratio.

In Example 1 the common ratio of is the similarity ratio of to ΔXYZ.

Is the similarity ratio the same From ΔXYZ to ΔRST?

You Try!

Given ΔJKL ~ ΔPQR, list all pairs of congruent angles. Write the ratios of the corresponding side lengths in a statement of proportionality.

Standardized Test Practice

Ex.2 Are the 2 triangles similar? If so, write a similarity statement. What is the similarity ratio from ΔCDE to ΔVUT?

YesΔCDE~ΔTUV

You Try!In the diagram, ΔABC ~ ΔDEF. Check that

the ratios of corresponding side lengths are equal. What is the scale factor from ΔABC to

ΔDEF? 𝟓𝟕

Standardized Test Practice

Scale Factor for Dilation

Is NOT the same as a

Similarity ratio

Congruent FiguresCongruent figures are also considered to be

similar figures. What would be the similarity ratio between any two congruent

figures?

1:1

Ex.3 Use Similar Polygons

I

Are there other Ways to set up a

Proportion in this problem?

In the diagram, ΔXYZ ~ ΔPQR. Solve for the missing side.

You Try!

25

HW Assignment

• Blue Workbook–Section 6.1 #19-24–Section 6.3 #1-4, 16-19

Proving Triangles Similar

Unit 13

SHORTCUTS

Angle-Angle (AA) Similarity Postulate

Examples of AA

Side-Side-Side (SSS) Similarity Postulate

Examples of SSS

Side-Angle-Side (SAS) Similarity Postulate

Examples of SAS

Are the triangles similar? Why or Why Not?

A few more…

Are these triangles similar? Why or Why not?

HW Assignment

Warm Up- Take Notes Over Videohttp://youtu.be/tm-_6sFdfk8

Practice

Partner Project

Proving Pythagorean Theorem

Using Similar Triangles

Unit 13

45.G.SRT.4

Proving the Pythagorean Theorem using Similar

Triangleshttp://www.khanacademy.org/math/geometry/triangles/v/pythagorean-theorem-proof-using-similarity

Assignment

Handout(Proving the Pythagorean Thm and Shadows)