QUADRILATERALS
Quadrilateral
- just means "four sides" (quad means four, lateral means side)
- A quadrilateral has four-sides, it is 2 dimensional (a flat shape), closed (the lines join up), and has straight sides.
PROPERTIES
A quadrilateral has:
- four sides (edges)
- four vertices (corners)
- interior angles that add to 360 degrees
TYPES OF QUADRILATERALS
THE RECTANGLE
A rectangle is a four-sided shape where every angle is a right angle (90 degrees)
Also opposite sides are parallel of equal length.
THE RHOMBUS
A rhombus is a four-sided shape where all sides have equal length.
Also opposite sides are parallel and opposite angles are equal.
THE SQUARE
A square has equal sides and every angle is a right angle (90 degrees).
Also opposite sides are parallel.
THE PARALLELOGRAM
A parallelogram has opposite sides parallel and equal in length.
Also opposite angles are equal.
THE TRAPEZOID /
THE ISOSCELES TRAPEZOID
The trapezoid has a pair of opposite sides parallel.
An Isosceles Trapezoid has left and right sides of equal length that join to the base of equal angles.
THE KITE
A Kite has two pairs of sides and each pair is made of two equal-length sides that join up.
The angles where the two pairs meet are equal.
TUTORIAL #1:Proving Parallelograms
THEOREMS
Theorem #1: If a quadrilateral is a parallelogram then its opposite sides are congruent.
Theorem #2: If a quadrilateral is a parallelogram then its opposite angles are congruent.
Theorem #3: If a quadrilateral is a parallelogram then its adjacent sides are supplementary.
Theorem #4: If a quadrilateral is a parallelogram then its diagonals bisects each other.
Theorem #5: If a quadrilateral is a parallelogram then its diagonals forms two congruent triangles.
THREE CONGRUENCE THEOREMS
SSS (SIDE-SIDE-SIDE) - If three sides of a triangle are congruent to three sides of another triangle, the triangles are congruent.
ASA (ANGLE-SIDE-ANGLE) - If two angles and the included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
SAS (SIDE-ANGLE-SIDE) - If two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
