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- Geometry Chapter 8 Vocabulary

Lexi A.

Polygon Interior Angles Theorm

the sum of the interior angles of a polygon equals (n-2)180 where n is the number of sides.

Corollary to Theorm 8.1

the sum of the interior angles of a quadrilateral is 360.

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Convex Polygons

a polygon whose sides do not contain any points inside the polygon.

Polygon Exterior Angles Theorm

the sum of the measures of exterior angles of a CONVEX polygon, one angle at each vertex, is 360.

Parallelogram

quadrilateral with both pairs of opposite sides parallel to each other.

Theorm 8.4

If PQRS is a parallelogram, then <P is congruent to <R & <Q is congruent to <S.

Theorm 8.5

If PQRS is a parallelogram, then its consecutive angles are supplementary.

Theorm 8.6

If a quadrilateral is a parallelogram, then its diagonols bisect each other.

Theorm 8.3

If a quadrilateral is a parallelogram, then PQ is congruent to RS & QR is congruent to PS.

Diagonal of a Polygon

a segment that joins two nonconsecutive verticies.

Theorm 8.7

If both pairs of opposite SIDES of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

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Theorm 8.8

If both pairs of opposite ANGLES of a quadrilateral are congruent, then the quadrilateral is a parallelogram.

Theorm 8.9

If one pair of opposlite sides of a quadrilateral are congruent & parallel, then the quadrilateral is a parallelogram.

Theorm 8.10

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Rhombus

parallelogram with 4 congruent sides.

Rhombus Corollary

a quadrilateral is a rhombus if and only if it has 4 congruent sides.

Theorm 8.11

a parallelogram is a rhombus if and only if its diagonols are perpendicular.

Theorm 8.12

a parallelogram is a rhombus if and onl if each diagonol bisects a pair of opposite sides.

Rectangle

parallelogram with 4 right angles.

Rectangle Corollary

a quadrilateral is a rectangle if and only if it has four right angles.

Theorm 8.13

a parallelogram is a rectangle if and only if its diagonols are congruent.

Square

parallelogram with 4 congruent sides and 4 right angles.

Square Corollary

a quadrilateral is a square if and only if it's a rhombus and a rectangle.

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