Isosceles Triangles & Coordinate Proof Advanced Geometry Triangle Congruence Lesson 3 Isosceles Triangles & Coordinate Proof

Example: Identify the legs, base, vertex angle, and base angles of each isosceles triangle.

Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. If , then . In other words, the base angles of an isosceles triangle are congruent.

Example: If , name two congruent angles. If , name two congruent segments.

Example: ABD is isosceles, and ACD is a right triangle. If what is ?

Example: is equilateral. Find x, , and .

figures are placed in the coordinate plane Coordinate Proof figures are placed in the coordinate plane use algebra to prove Slope Formula Midpoint Formula Distance Formula

Example: Name the missing coordinates of each triangle.

Placing Figures in the Coordinate Plane Suggestions: Use the origin as a vertex. Place at least one side on an axis. Keep the figure in the first quadrant if possible. Use coordinates that make computations as simple as possible.

Example: Position and label each triangle on the coordinate plane. isosceles with base that is 2b units long equilateral with sides a units long

Coordinate Proof Tami and Juan are hiking. Tami hikes 300 feet east of camp and then hikes 500 feet north. Juan hikes 500 feet west of camp and then 300 feet north. Prove that Juan, Tami, and the camp form a right triangle.

If a line segment joins the midpoint of two sides of a triangle, then it is parallel to the third side.