Cheatography

# Geometry Unit 6 Cheat Sheet by CCRoses

Holt McDougal Geometry Unit 6

### Polygons

 Number of Sides Name of Polygon 3 Triangle 4 Quadri­lateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

### Vocabulary

 Term Definition Vertex of the polygon The common endpoint of two sides of a polygon Diagonal A segment connecting any two noncon­sec­utive vertices of a polygon Regular polygon An equila­teral and equian­gular polygon (always convex) Concave polygon A polygon with parts of a diagonal on the exterior of the polygon Convex polygon A polygon with every part of the diagonals on the interior Rectangle A quadri­lateral with four right angles Rhombus A quadri­lateral with four congruent sides Square A quadri­lateral with four right angles and four congruent sides; it is a parall­elo­gram, a rectangle, and a rhombus Kite A quadri­lateral with exactly two pairs of consec­utive sides Trapezoid A quadri­lateral with exactly one pair of parallel sides Base One of the parallel sides of a trapezoid Leg One of the nonpar­allel sides of a trapezoid Isosceles trapezoid A trapezoid in which the legs are congruent Midsegment of a trapezoid The segment whose endpoints are the midpoints of the legs of a trapezoid

### Theorems & Postulates

 Name Theorem Polygon angle sum theorem The sum of the interior angle measures of a convex polygon with n sides is (n - 2)180 degrees. Polygon exterior angle sum theorem The sum of the exterior angle measures, one angle at each vertex, of a convex polygon is 360 degrees. Trapezoid Midsegment Theorem The midsegment of a trapezoid is parallel to each base, and its length is one half the sum of the lengths of the bases

### Formulas

 Name Formula Sum of interior angle measures (n - 2)180 Midsegment of a trapezoid length 1/2(base 1 + base 2) Midpoint Formula (x,y) = [(x1 + x2)/2], [(y1 + y2)/2] Distance formula √(x2 − x1)2+(y2 − y1)2

### Properties of Parall­elo­grams

 If a quadri­lateral is a parall­elo­gram, then... Its opposite sides are congruent AND Its opposite angles are congruent AND Its consec­utive angles are supple­mentary AND Its diagonals bisect each other. If... One pair of opposite sides of a quadri­lateral are parallel and congruent OR Both pairs of opposite sides of a quadri­lateral are congruent OR Both pairs of opposite angles of a quadri­lateral are congruent OR An angle of a quadri­lateral is supple­mentary to both of its consec­utive angles OR The diagonals of a quadri­lateral bisect each other, then the quadri­lateral is a parall­elo­gram.

### Properties of Rectangles & Rhombuses

 If a quadri­lateral is a rectangle, then... It is a parall­elogram AND Its diagonals are congruent. If a quadri­lateral is a rhombus, then... It is a parall­elogram AND Its diagonals are perpen­dicular AND Each diagonal bisects a pair of opposite angles.

### Properties of Kites and Trapezoids

 If a quadri­lateral is a kite, then... Its diagonals are perpen­dicular AND Exactly one pair of opposite angles are congruent. If a quadri­lateral is an isosceles trapezoid, then... Each pair of base angles are congruent AND Its diagonals are congruent. If... A trapezoid has one pair of congruent base angles OR A trapezoid has congruent diagonals, then the trapezoid is isosceles.