Topic 6 Vocabulary Geometry

Polygon

A plane figure that meets the following conditions:

• It’s formed by three or more segments called sides, such as no two sides with common e splints are collinear

• Each side intersects exactly two other sides, one at each endpoint

Sides

The segments that form the polygon

Vertex

An endpoint of a side of the polygon

Convex

No line that contains a side of the polygon contains a point in the interior of the polygon

Concave

A polygon that is not convex

Equilateral

All sides of the polygon are congruent

Equiangular

All interior angles of the polygon are congruent

Regular

Occurs when a polygon is equilateral and equiangular

Diagonal

A segment that joins two nonconsecutive certified

Quadrilateral Sum Conjecture

The sum of the measures of the 4 angles of any quadrilateral is 360 degrees

Pentagon Sum Conjecture

The sum of the measures of the 5 angles of any pentagon is 540 degrees

Polygon Sum Conjecture

The sun if the measures of the n-interior angles of an n-gon is 180(n-2)

• To find the measures of the interior angles we use 180(n-2)/n

• To find the measures of the exterior angles we use 180-180(n-2)/n

Parallelogram

Is a quadrilateral with both pairs of opposite sides parallel

Parallelogram Opposite Angles Conjecture

Opposite angles in a parallelogram are congruent

Parallelogram Consecutive Angle Conjectures

Adjacent angles in a parallelogram are supplementary

Parallelogram Opposite Sides Conjectures

Opposite sides of a parallelogram are equal in length

Parallelogram Diagonals Conjecture

The diagonals of a parallelogram are bisected by the point of their intersection

Opposite Sides Theorem Converse

If the opposite sides of a quadrilateral are congruent, then the figure is a parallelogram

Opposite Angles Theorem Converde

If the opposite angles of a quadrilateral are congruent, then the figure is a parallelogram

Consecutive Angles Theorem Converse

If the consecutive angles of a quadrilateral are supplementary, then the figure is a parallelogram

Diagonals Theorem Converse

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

Rhombus

A parallelogram with 4 congruent sides

Rectangle

A parallelogram with 4 right angles

Square

A parallelogram with 4 congruent sides and 4 right angles

Rhombus Diagonals Conjecture

The diagonals of a rhombus are perpendicular and they bisect each other

Rhombus Angles Conjecture

The diagonals of a rhombus bisect the angles of a rhombus

Theorem 6.12 A

A parallelogram is a rhombus if, and only if, it’s diagonals are perpendicular

Theorem 6.12 B

A parallelogram is a rhombus if, and only if, each diagonal bisects a pair of opposite angles

Rectangle Diagonals Conjecture

The diagonals of a rectangle are congruent, and bisect each other

Theorem 6.13 A

A parallelogram is a rectangle if, and only if, it’s diagonals are congruent

Square Diagonals Conjecture

The diagonals of a square are congruent, perpendicular, and bisect each other

Trapezoid

A quadrilateral with exactly one pair of parallel sides

Bases of a Trapezoid

The parallel sides of a trapezoid

Base Angles of a Trapezoid

A trapezoid has two pairs of base angles. Each pair of base angles shares a side

Legs of a Trapezoid

The non-parallel sides

Isosceles Trapezoid

A trapezoid with congruent legs

Midsegment of a Trapezoid

The segments that connect the midpoints to the legs

Theorem 6.14

If a trapezoid is isosceles, then each pair of base angles is congruent

Theorem 6.16

A trapezoid is isosceles if, and only if, it’s diagonals are congruent

• The consecutive angles between the bases of a trapezoid are supplementary

• The mid-segment of a trapezoid is parallel to each base and its length is ½ the sun of the length of the bases

Kite

A quadrilateral that has two pairs of consecutive congruent sides, but it’s opposite are not congruent

Vertex Angles

The two angles between each pair of congruent sides

Kite Angles Conjecture

Non-vertex angles are congruent

Kite Diagonals Conjecture

Diagonals of a kite are perpendicular

Kite Diagonals Bisector Conjecture

The diagonals connected the vertex angles of a kite is the perpendicular bisector of the other diagonal

Kite Angle Bisector Conjecture

The vertex angles of a kite are bisected by a diagonal