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

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

3. 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.

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

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

6. Example:
is equilateral. Find x,
, and .

7. 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

8. Example: Name the missing coordinates of each triangle.

9. 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.

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

11. 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.

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