Download 3 Triangle Similarity: AA, SSS, and SAS

7- 3 Triangle Similarity: AA, SSS, and SAS
When two triangles have 2 pairs of congruent angles, the third pair must be congruent too.
The lengths of the triangles are in proportion.
Angle-Angle (AA~) Similarity Postulate—If two angles of one triangle are congruent to two
angles of another triangle, then the triangles are similar.
~
http://www.google.com/imgres?q=aa+similarity+postulate&num=10&
How is this AA ~ ?
Side-Angle-Side (SAS~) Similarity Theorem—if an angle of one triangle is congruent to an
angle of another triangle, and the sides including these angles are in proportion, then the
triangles are similar.
If < V is congruent to <L, and UV = WV, then triangle UVW ~ triangle KL
KL ML
Make sure you put the “~” mark when using similarity !!!
Side-Side-Side (SSS~) Similarity Theorem --If all corresponding sides of two
triangles are in proportion, then the triangles are similar
If AB = BC = CA, then triangle ABC ~ triangle HJK
HJ JK
KH
Properties of Similarity
1. Reflexive Property of Similarity
ABC ~
ABC
2. Symmetric Property of Similarity
If
ABC ~
DEF, then
DEF ~
ABC
3. Transitive Property of Similarity
If
ABC ~
DEF and
DEF ~
XYZ, then
ABC ~
XYZ
PROOF
Given: BC ll to DE
Prove: Triangle ABC ~ Triangle ADE
Statement
Reason
1. BC ll DE
1. Given
2. <A is congruent to <A
2. Reflexive
3. <B is congruent to <D
3. Corresponding <’s
4. <C is congruent to < E
4. Corresponding <’s
5. Triangle ABC ~ Triangle ADE
5. AA Similarity Postulate