Key Concepts: Triangles and Coordinate Proof ⭐

Coordinate Proofs with Triangles

In a coordinate proof involving triangles, you place the Triangle on the coordinate Plane and use formulas to prove properties.

Strategies for Placing Triangles

• Place one vertex at the origin (0, 0).
• Align one side along the x-axis or y-axis.
• Use variables (a, b, c) for coordinates to prove general results.
• For isosceles triangles, use the y-axis as the Line of symmetry.

Common Proofs

• Prove a Triangle is isosceles: Show two sides have equal length using the Distance Formula.
• Prove a Triangle is right: Show two sides have perpendicular slopes (product = −1).
• Find the centroid: Average the coordinates: ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).