Coordinate Proofs Geo H

parallelgram

use one of the following :

1. diagonals bisect each other

2. both pairs of opposite sides are parallel

3. both pairs of opposite sides are congruent

4. one pair of opposite sides are parallel and congruent

Rectangle

One of ways to prove a parallelogram and one of the following :

1. one right angle

2. diagonals are congruent

Rhombus

One of ways to prove a parallelogram and one of the following :

1. Diagonals are perpendicular

2. two adjacent sides are congruent

Square

prove figure is a rectangle (you must prove parallelogram first) and two adjacent sides are congruent

or

prove figure is a rhombus (you must prove parallelogram first) and has one right angle

Trapezoid

prove one pair of opposite sides are Parallel and the other pair of opposite sides are not parallel

Isosceles Trapezoid

Prove the figure is a Trapezoid and one of the following:

1. legs are congruent

2. Diagonals are congruent

Kite

prove 2 consecutive sides are congruent and opposite sides are not congruent

to prove line segments are congruent

use distance formula / d= (x₂-x₁)² + (y₂-y₁)²

to prove lines parallel or perpendicular

use slope formula/

to prove line segments bisect each other

use midpoint formula/ M_x= x₁ + x₂ / 2

Right trapezoid

prove figure is a trapezoid and one leg is perpendicular to a base