Geometry Unit 7 Polygons & Quadrilaterals – Flashcards

The sum of the degrees in any polygon can be determined by the number of triangles that can be drawn within the polygon.

A closed 2-D figure formed by three or more line segments.

Sum = (Number of sides - 2) times 180 s= (n-2)*180

A polygon that is convex, equilateral, and equiangular.

All angles are congruent in a regular polygon so take the Sum of the interior angles and divide it by the Number of sides. interior angle = s/n

The ___________ are always supplementary to their adjacent interior angle.

The __________ is always 360 degrees.

360 divided by the Number of sides exterior angle = 360/n

360 divided by the measure of one exterior angle n = 360/exterior angle

A polygon with three sides.

A polygon with four sides.

A polygon with five sides.

A polygon with six sides.

A polygon with seven sides.

A polygon with eight sides.

A polygon with nine sides.

A polygon with ten sides.

A polygon with twelve sides.

A polygon with N sides.

1) Opposite sides are parallel. 2) Opposite sides are congruent. 3) Opposite angles are congruent. 4) Consecutive angles are supplementary. 5) Diagonals bisect each other.

Sides the never touch because they have the same slope.

Sides with the same length.

Angles with the same measure (degrees).

Angles of a polygon that share a common side.

Angles whose sum equals 180 degrees.

Segments that join non-consecutive vertices.

To divide into two equal parts.

1) Prove both pairs of opposite sides are congruent, using the distance formula. 2) Proving both pairs of opposite sides are parallel, using the slope formula. 3) Prove one pair of opposite sides are congruent and parallel, using both the distance and slope formulas.

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

change in the y's (rise) over the change in x's (run) m = (y₂- y₁) / (x₂- x₁)

All of the properties of parallelograms plus two more: 1) Opposite sides are parallel. 2) Opposite sides are congruent. 3) Opposite angles are congruent. 4) Consecutive angles are supplementary. 5) Diagonals bisect each other. 6) All four angles are right angles. 7) Diagonals are congruent.

All of the properties of parallelograms plus three more: 1) Opposite sides are parallel. 2) Opposite sides are congruent. 3) Opposite angles are congruent. 4) Consecutive angles are supplementary. 5) Diagonals bisect each other. 6) All four sides are congruent. 7) Diagonals are perpendicular. 8) Diagonals bisect opposite angles.

All the properties of parallelograms, rectangles, and rhombi: 1) Opposite sides are parallel. 2) Opposite sides are congruent. 3) Opposite angles are congruent. 4) Consecutive angles are supplementary. 5) Diagonals bisect each other. 6) All four angles are right angles. 7) Diagonals are congruent. 8) All four sides are congruent. 9) Diagonals are perpendicular. 10) Diagonals bisect opposite angles.

Step 1: Check congruency of sides, using the distance formula. Step 2: Check congruent of diagonals, using the distance formula.

Opposite sides are congruent BUT diagonals are NOT congruent.

Opposite sides are congruent AND diagonals are congruent.

All four sides are congruent BUT diagonals are NOR congruent.

All four sides are congruent AND diagonals are congruent.

1) Only ONE pair of opposite sides are parallel. 2) Consecutive angles are supplementary.

All the properties of non-isosceles trapezoids plus four more... 1) Only ONE pair of opposite sides are parallel. 2) Consecutive angles are supplementary. 3) Non-parallel sides (legs) are congruent. 4) Diagonals are congruent. 5) Base angles are congruent. 6) Opposite angles are supplementary.

The parallel sides of a trapezoid.

The nonparallel sides of a trapezoid.

A segment that connects the midpoints of the legs. It's length is the average of the trapezoid's bases.

1) Exactly two pairs of consecutive congruent sides. 2) One pair of opposite angles are congruent. 3) Diagonals are perpendicular.