Download Sec 2 5.2 AA, SSS, SAS Similarity 5.2

Sec 2
5.2
AA, SSS, SAS Similarity
5.2
SIMILAR TRIANGLES have the same shape but can be different sizes (or rotated/reflected)
a) Angles are congruent (same measure)
b) Sides are proportional (same scale factor)
1) If 2 triangles are congruent, are they similar?
If 2 triangles are similar, are they congruent?
2) Find all angles and side lengths give that ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹 (← 𝑠𝑖𝑚𝑖𝑙𝑎𝑟𝑖𝑡𝑦 𝑠𝑡𝑎𝑡𝑒𝑚𝑒𝑛𝑡 )
Ways to prove similarity:
Angle-Angle (AA) - If two angles of one triangle are congruent (equal) to two angles of another triangle, then
the triangles are SIMILAR.
Side-Side-Side (SSS) - If the measures of the corresponding sides of two triangles are proportional (scale
factor), then the triangles are SIMILAR
Side-Angle-Side (SAS) - If the measures of two sides of a triangle are proportional (scale factor) to the
measures of two corresponding sides of another triangle, and the included angles (between these corresponding
sides) are congruent, then the triangles are SIMILAR.
AA
SSS
SAS
5
3
15
9
Determine whether the triangles are similar. Write a similarity statement (ex: ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹) if they are similar.
Write “not similar” if the triangles are not similar.
3)
4)
a) AA/SAS/SSS
b) Prove it:
a) AA/SAS/SSS
b) Prove it:
c) Similarity statement:
c) Similarity statement:
5)
6)
7)
a) AA/SAS/SSS
b) Prove it:
a) AA/SAS/SSS
b) Prove it:
a) AA/SAS/SSS
b) Prove it:
c) Similarity statement:
c) Similarity statement:
c) Similarity statement:
9)
10)
8)
a) AA/SAS/SSS
b) Prove it:
c) Similarity statement:
a) AA/SAS/SSS
b) Prove it:
c)Similarity statement:
The following triangles are similar. Find the missing length.
11)
12)
a) AA/SAS/SSS
b) Prove it:
c) Similarity statement: