Geometry

AnglesParallel LinesTrianglesQuadrilaterials– ParallelogramsAreaCirclesVolume

Types of Angles

• Classification– Acute: all angles are less than 90°– Obtuse: one angle is greater than 90°– Right: has one angle equal to 90°

• Complementary: the sum of two angles is 90°

• Supplementary: the sum of two angles is 180°

• Adjacent: angles that share a side• Linear Pair: angles that are both supplementary

and adjacent

Congruent Angle Pairs formed by

Parallel Lines

Alternate interior angles

• <3 & <6, <4 & < 5

Alternate exterior angles

• <1 & <8, <2 & <7

Corresponding angles

• <1 & <5, <2 & <6, <3 & <7, <4 & <8

Vertical angles

• <1 & <4, <2 & <3, <5 & <8, <6 & <7

1 23 4

5 67 8

Angles that are both on the same side of the transversal and either both interior or exterior

• <3 & <5, <4 & < 6, <1 & <7, <2 & < 8

Linear Pair

• <1 & <2, <2 & <4, <3 & <4, <1 & <3,

<5 & <6, <6 & <8, <7 & <8, <5 & <7

1 23 4

5 67 8

Supplementary Angle Pairs formed by

Parallel Lines

Polygons

• The sum of the interior angles: (n - 2)(180°)• Classified by number of sides (n)

– Triangle (3)– Quadrilateral (4)– Pentagon (5)– Hexagon (6)– Heptagon (7)– Octagon (8)– Nonagon (9)– Decagon (10)

• Regular Polygon: all sides are congruent

Triangles

• The sum of the angles in a triangle is 180°

• a – b < third side < a + b

• The sum of the two remote interior angles is equal to the exterior angles

• Types:

Two sides are equal One

Right angle

All sides are equal

Scalene Isosceles Equilateral Right

No sides are equal

QUADRILATERALS

PARALLELOGRAM

Both pairs of opposite sides are parallel

TRAPEZOIDS

Only one pair of Opposite sides parallel

ISOSCLESTRAPEZOID

A trapezoid that hastwo equal sides

ROMBUS4 equal sides

RECTANGLE

4 right angles

SQUARE

Both a rhombusand a rectangle

Properties of Parallelograms

Diagonals are perpendicular to each other

Diagonals bisect their angles

Diagonals are congruent to each other

Diagonals bisect each otherOpposite sides are congruentOpposite angles are congruentDiagonals bisect each otherConsecutive angles are supplementaryDiagonals form two congruent triangles

Area

½bh bh

lw

s2

½(b1 + b2 )

Circles

• Exact: express in terms of π• Approximate: use an approximation of π (3.14)

Circumference

C = 2πr or C = πd

A = πr2

Volume

General Formula: V = (area of base)(height)

3

1

3

1

e3

πr2hπr2hlwh

Bh

3

4πr3