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