Geometry – 4.4 Proving Triangles Congruent – SSS , SAS

Postulate 4.1 - SSS Postulate

If __________ sides of one triangle are __________________ to ____________

sides of a _______________ triangle, then the triangles are _______________.

Side 𝐴𝐵 ≅ _________

Side 𝐵𝐶 ≅ _________

Side 𝐴𝐶 ≅ _________

Then ∆𝐴𝐵𝐶 ≅ ___________

Included Angle:

Postulate 4.2 – SAS Postulate

If____________ sides and the _________________ angle of one triangle are

__________________ to ___________ sides and the ___________________ angle of a

second triangle, then the triangles are ___________________.

Side 𝐴𝐵 ≅ ____________

Angle ∠𝐵 ≅ ___________

Side 𝐵𝐶 ≅ ____________

Then ∆𝐴𝐵𝐶 ≅ _______________

Geometry – 4.4 Proving Triangles Congruent – SSS , SAS

Example 1: Identify Congruent Triangles

Determine which postulate can be used to prove that the triangles are congruent. Also, name the

congruent sides and angles if any.

a. b.

c. d.

e. f.

Geometry – 4.4 Proving Triangles Congruent – SSS , SAS

Example 2: SSS on a Coordinate Plane

a. Triangle ABC has vertices A(1, 1), B(0, 3), and C(2, 5). Triangle EFG has vertices E(1, -1), F(2, -5)

and G(4, -4). Determine if the triangles are congruent.

b. Triangle JKL has vertices J(2, 5), K(1,1), and L(5,2). Triangle NPQ has vertices N(-3,0), P(-7,1) and

Q(-4.4). Determine if the triangles are congruent.