Similarity in Triangles Unit 13 Notes Definition of Similarity.

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Presentation transcript:

Similarity in Triangles Unit 13 Notes

Definition of Similarity

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 Ratio

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?

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?

Standardized Test Practice

Congruent Figures Congruent figures are also considered to be similar figures. What would be the similarity ratio between any two congruent figures?

Ex.3 Ex.3 Use Similar Polygons I

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

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

Proving Triangles Similar Unit 13

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 Video

Practice

Partner Project

Proving Pythagorean Theorem Using Similar Triangles Unit G.SRT.4

Proving the Pythagorean Theorem using Similar Triangles

Assignment Handout (Proving the Pythagorean Thm and Shadows)