4.8 Triangles and Coordinate Proofs

Coordinate Proofs Coordinate proofs use figures in the coordinate plane and algebra to prove geometric concepts. The first step in a coordinate proof is placing the figure on the coordinate plane.

Example 1 a) Position and label right triangle XYZ with leg d units long on the coordinate plane.

Example 1 b) Which would be the best way to position and label equilateral triangle ABC with side w units long on the coordinate plane?

How To Place Triangles on a Coordinate Plane

Example 2 Name the missing coordinates of isosceles right triangle QRS.

Example 3 Position an isosceles triangle on the coordinate plane so that its sides are a units long and one side is on the positive x-axis.

Example 4 Name the missing coordinates of each triangle.

Example 4 Name this missing coordinates of each triangle.

Example 4 Name the missing coordinates of each triangle.

Example 5 Position and label each triangle on the coordinate plane. a) isosceles triangle △RST with base (RS) 4a units long

b. isosceles right △DEF with legs e units long

c. equilateral triangle △EQI with vertex Q(0, √3b) and sides 2b units long

Summary

Summary

Summary