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
If two polygons are similar, then the ratio of the
lengths of two corresponding sides is called
the Similarity Ratio.
5
3
In Example 1 the common ratio of is the similarity
ratio of Δ𝑅𝑆𝑇 to ΔXYZ.
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 Use Similar Polygons
I
You Try!
In the diagram, ΔXYZ ~ ΔPQR.
Solve for the missing side.
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
http://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 Triangles
http://www.khanacademy.org/math/geometry/triangles/v/pythagorean-theorem-proof-using-similarity
Assignment
Handout
(Proving the Pythagorean Thm and Shadows)