1. 4.3 – Prove Triangles Congruent by SSS

2. We know…
Triangles have six parts
But do we really need all six parts to say two triangles are congruent?

3. Side-Side-Side (SSS) Congruence PostulateB
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
If Side
Side
Then C A S T R

4. Use the SSS Congruence Postulate
EXAMPLE 1
Use the SSS Congruence Postulate
Decide whether the congruence
statement is true.
Explain your reasoning.
SOLUTION
Given
Given
Reflexive Property
So, by the SSS Congruence Postulate,

5. Use the SSS Congruence Postulate
EXAMPLE 2
Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning.
ACB CAD
SOLUTION
It is given that BC AD By Reflexive property
AC AC, But AB is not congruent CD.
Therefore, the triangles are not congruent.

6. EXAMPLE 3
Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning.
DFG HJK

7. Use the SSS Congruence Postulate
EXAMPLE 4
Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning. A B C D

9. Use the SSS Congruence Postulate
EXAMPLE 5
Use the SSS Congruence Postulate
Decide whether the congruence statement is true. Explain your reasoning. A B C D

10. Use the SSS Congruence Postulate
EXAMPLE 6
Use the SSS Congruence Postulate
has vertices J(-3, -2), K(0, -2), and L(-3, -8).
has vertices R(10, 0), S(10, -3), and T(4, 0).
Graph the triangles in the same coordinate plane and show that they are congruent.
SOLUTION
Use the distance formula to find the lengths of the diagonal segments.
LK = TS =6.7 (By distance formula)
KJ = SR = 3. (By counting)
JL = RT = 6. (By counting)
Therefore, by SSS, the triangles are congruent.

11. Use the SSS Congruence Postulate
EXAMPLE 7
Use the SSS Congruence Postulate
has vertices P(-5, 4), Q(-1, 4), and R(-1, 1).
has vertices A(2, 5), B(2, 1), and C(5, 1).
Graph the triangles in the same coordinate plane and show that they are congruent.
STEP 1: Graph
STEP 2: Use the distance formula to find the lengths of the diagonal segments.
PR =
AC =
PR = _____ =______ (By ______________)
PQ =_____ = _____ (By_____________)
QR = _____ = _____ (By ____________)
Therefore, by ______, _________________________.