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Level 117

Ways to Prove Congruence


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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