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Relationships Between Points

two points must be collinear

Determine a Plane

three noncollinear points determine a plane

Relationships Between Lines in Planes

either two lines are parallel or they intersect in exactly one point

Relationships Between Line and Plane

either a line and a plane are parallel, or they intersect in exactly one point or the plane contains the line

Relationships Between Two Planes

either two planes are parallel, or they intersect in a line

Ways to Prove Parallel Lines

show a pair of corresponding angles are congruent

SSS Postulate

all sides will marked congruent to the corresponding sides of a second triangle

Ways to Prove Two Angles Congruent

identify two triangles in which the two segments or angles are corresponding parts

CPCTC

Corresponding parts of congruent triangles are congruent.

Ways to Prove a Parallelogram

if both pairs of opposite sides of a quadrilateral are parallel, then it is a parallelogram

Parallelogram Ways to Prove

Ways to prove a quadrilateral is a Parallelogram:

Parallelogram Properties

Properties of Parallelograms:

Parallelogram Definition

A four sided figure with two sets of parallel lines

Trapezoid Definition

A Quadrilateral with exactly one set of parallel sides

Trapezoid Ways to Prove

-show only one set of opposite sides are parallel

Trapezoid Properties

- the two sides that are not parallel are the legs

Isosceles trapezoid

A trapezoid with two parallel sides (per usual) and congruent legs. The congruent legs cause congruent base angles.

Rhombus Definition

Parallelogram with 4 congruent sides

Rhombus Properties

-All characteristics of parallelograms plus

Rhombus Ways to Prove

-Prove that all four sides are parallel

Kite Definition

Quadrilateral with consecutive sides and no parallel sides

Kite Ways to Prove

-Exactly one diagonal is bisected

Kite Properties

-2 sets of congruent sides

Rectangle Definition

A Quadrilateral with all right angles, but is not a square

Rectangle Ways to Prove

Prove that all angles are right angles

Rectangle Properties

- 2 sets of parallel sides

Square Definition

A Quadrilateral with 4 congruent sides and 4 right( congruent) angles

Square Ways to Prove

-Prove all four sides are congruent and all angles are congruent

Square Properties

-Four right angles