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AA, SSS, AND SAS SIMILARITY6.2
WARM UP• Solve the proportions
A) 68
= 2𝑚𝑚
B) 8𝑣𝑣
= 36
C) 62
= 4𝑏𝑏−7
D) 65
= 𝑣𝑣+13
LESSON 6.2: AA, SSS, SAS 2
OBJECTIVES• Determine whether two triangles are SIMILAR
Similarity Statements �𝐴𝐴𝐴𝐴𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝐴𝐴𝑆𝑆
• Understand and use SIMILAR triangle properties
LESSON 6.2: AA, SSS, SAS 3
SIMILAR TRIANGLES• Triangles are SIMILAR if they have the same shape, but can be
different sizes (can also be rotated or reflected)
PROPERTIES• Correspond angles are congruent (same measure)• Corresponding sides are all in the same proportion (k)
LESSON 6.2: AA, SSS, SAS 4
SIMILAR TRIANGLES• CONGRUENT triangles have corresponding parts with both
angle measures and side lengths that are the same.
1) If 2 triangles are congruent, are they similar?
If 2 triangles are similar, are they congruent?
LESSON 6.2: AA, SSS, SAS 5
SIMILAR TRIANGLES
LESSON 6.2: AA, SSS, SAS 6
SIMILAR TRIANGLES
LESSON 6.2: AA, SSS, SAS 7
F i n d a l l
a n g l e s a n d s i d e
l e n g t h s
g i v e n
1 1 2 o
6 0 o
2 8
36
2 0
2)
SIMILAR TRIANGLES• What is the minimum amount of information needed to prove
that two triangles are similar?
In other words, how much information can I take away before we no longer know they are similar?
LESSON 6.2: AA, SSS, SAS 8
ANGLE-ANGLE• Angle-Angle (AA)
• If two angles of one triangle are congruent (equal) to two angles of another triangle, then the triangles are SIMILAR.
LESSON 6.2: AA, SSS, SAS 9
SIDE-SIDE-SIDE• Side-Side-Side (SSS)
• If the measures of the corresponding sides of two triangles are proportional (scale factor), then the triangles are SIMILAR
LESSON 6.2: AA, SSS, SAS 10
SIDE-ANGLE-SIDE• 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.
LESSON 6.2: AA, SSS, SAS 11
53 15
9
AA, SSS, SAS SIMILARITY3) Determine whether the triangles are similar. Write a similarity statement.
LESSON 6.2: AA, SSS, SAS 12
AA, SSS, SAS SIMILARITY4) Determine whether the triangles are similar. Write a similarity statement.
LESSON 6.2: AA, SSS, SAS 13
AA, SSS, SAS SIMILARITY5) Identify the similar triangles and then find the value of 𝑥𝑥.
LESSON 6.2: AA, SSS, SAS 14
AA, SSS, SAS SIMILARITYAre the following similar triangles? If so, state how you know and write a similarity statement.6) 7) 8)
LESSON 6.2: AA, SSS, SAS 15
AA, SSS, SAS SIMILARITYAre the following similar triangles? If so, state how you know and write a similarity statement.9) 10)
LESSON 6.2: AA, SSS, SAS 16
AA, SSS, SAS SIMILARITYThe following triangles are similar. Find the missing length.11) 12)
LESSON 6.2: AA, SSS, SAS 17
HOMEWORKWorksheet 6.2
LESSON 6.2: AA, SSS, SAS 18