Download 7.3 – Postulates and Theorems Postulate 7.1 (Angle

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7.3 – Postulates and Theorems
Postulate 7.1 (Angle-Angle (AA) Similarity) – If the two angles of one triangle are congruent
to the two angles of another triangle, then the triangles are similar.
Example: ∠P ≅ ∠T and ∠Q ≅ ∠S, so triangle PQR ~ triangle TSU
S
Q
P
R
T
U
Theorem 7.1 (Side-Side-Side (SSS) Similarity) – If the measures of the corresponding sides of
two triangles are proportional, then the triangles are similar.
𝑷𝑸
𝑸𝑹
𝑹𝑷
Example: 𝑺𝑻 = 𝑺𝑼 = 𝑼𝑻 so triangle PQR ~ triangle TSU
S
Q
a
P
b
c
ax
R
T
bx
cx
U
Theorem 7.2 (Side-Angle-Side (SAS) Similarity) – If the measures of two sides of a triangle
are proportional to the measures of two corresponding sides of another triangle and the included
angles are congruent, then the triangles are similar.
𝑷𝑸
𝑸𝑹
Example: 𝑺𝑻 = 𝑺𝑼 and ∠Q ≅ ∠S, so triangle PQR ~ triangle TSU
S
Q
a
P
b
c
ax
R
T
bx
cx
Theorem 7.3 – Similarity of triangles is reflexive, symmetric, and transitive.
U
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