Geometry Chapter 6 Properties, Theorems, Definitions

Flashcards for geometry chapter 6 test

Polygon

A closed figure that is the union of three or more line segments

Diagonal

A line segment that connects one vertex to any other non-consecutive vertex

Number of Diagonals

3 less than the number of sides

Number of Triangles

2 less than the number of sides

Polygon Angle-Sum Theorem

The sum of the measures of the interior angles of a polygon is 180(n-2)

Equilateral

All sides are congruent

Equiangular

All angles are congruent

Regular

Equilateral and Equiangular

Corollary to the Polygon Angle-Sum Theorem

The measure of each interior angle of a regular polygon is 180(n-2)/n or sum of interior angles/n

Polygon Exterior Angle-Sum

The sum of exterior angles in any polygon is 360

Opposite sides

Sides that do not share a vertex

Consecutive/adjacent sides

Sides that share a common vertex

Opposite vertices

Vertices that are not connected by a side

Consecutive/adjacent vertices

Vertices that are the endpoints of the same side

Parallelogram Properties (THE BIG 5)

• Opposite sides are congruent

• Opposite sides are parallel

• Opposite angles are congruent

• Consecutive/adjacent angles are supplementary

• Diagonals bisect eachother

Rectangle

• A parallelogram with 4 right angles (equiangular)

• Diagonals are congruent

• BIG 5 PROPERTIES

Rhombus

• A parallelogram with 2 congruent consecutive sides (equilateral)

• Diagonals are perpendicular

• Diagonals bisect opposite angles

Square

• Rectangle with 2 congruent consecutive sides

• Rhombus with 4 right angles

• Diagonals are perpendicular and congruent

• Diagonals bisect the opposite angles

Trapezoid

• There is only two parallel sides

• The parallel sides are called bases

• The non-parallel sides are called legs

Isosceles Trapezoid

• The legs are congruent

• The bases are congruent

• The midsegment is parallel to the bases

• The midsegment is ½ the length of the sum of the bases

Right Trapezoid

• One leg is perpendicular to the bases

Kite

• Quadrilateral with 2 pairs of congruent consecutive sides and no opposite sides congruent

• Diagonals are perpendicular

• The diagonals bisect the angles included in each pair of congruent consecutive lines.