Chapter 2

Chapter 0 Vocabulary Terms

Symmetry

when an object can be rotated or reflected and still appear the same

Rotational

rotating an object less than 360 about a point - retains shape and appearance

Reflectional

reflecting an object over a line and it retains original shape and appearance

Bilateral

when there is only 1 line of symmetry possible for a particular shape

Chapter 1 Vocabulary Terms

Note: The Basic Building Blocks of Geometry are points, lines, and planes.

Acute Angle

an angle measurement less than 90 degrees

Adjacent

angles sharing a side or sides sharing a vertex

Altitude

the height of a figure (always perpendicular to the base of the figure)

Angle

a geometric figure formed by two rays that have a common endpoint

Bisect

to divide into two equal parts

Collinear

points on the same line

Complementary

two angles whose measures have a sum of 90

Concave

hollow; curved inward, creating a hollow space; opposite of convex

Congruent

having the same size and shape

Consecutive

2 sides that share an angle or 2 angles that are the endpoints of 1 side

Convex

A polygon in which all vertices appear to be pushed outward.

Coplanar

lying in the same plane

Diagonal

a line segment connecting any 2 non-consecutive vertices of a polygon

Equal

having the same value

Equiangular

a polygon having all angles equal

Equilateral

a polygon having all sides or faces equal

Exterior Angles

angles on the outside of a polygon

Interior Angles

angles on the inside of a polygon

Isosceles

a polygon with at least two congruent sides

Line Segment

part of a line that is bounded by two end points

Linear Pair

two angles that are adjacent (on the same line) and supplementary

Midpoint

a point equidistant from the endpoints

Obtuse

an angle measurement above 90 but below 180 degrees

Parallel

being everywhere equidistant and not intersecting

Perpendicular

intersecting at or forming right angles

Polygon

closed plane figure having angles and straight sides

Ray

a straight line extending from a point

Reflex Angle

the difference between any angle and 360 degrees (360 30 = 330 reflex)

Regular Polygon

a polygon with all sides and all angles equal

Right Angle

an angle with the measure of 90 degrees

Scalene

a polygon with no congruent sides

Supplementary

two angles whose sum measures 180 degrees

Transversal

A line or segment crossing two or more parallel lines

Vertex

the point of intersection of lines or the point opposite the base of a figure

Vertical Angles

a pair of opposite congruent angles formed by intersecting lines

Types of Triangles

Classified by Their Sides

Scalene

triangle with no congruent sides

Isosceles

triangle with at least two congruent sides

Equilateral

a triangle having all sides or faces equal (also, all angles are congruent)

Classified by Their Angles

Acute

a triangle having all angles measuring less than 90 degrees

Right

a triangle with exactly 1 right angle

Obtuse

a triangle with exactly 1 obtuse angle

Special Quadrilaterals

Kite

two pairs of adjacent sides congruent and no opposite sides congruent

Parallelogram

a quadrilateral whose opposite sides are both parallel and equal in length

Rectangle

a parallelogram with four right angles

Rhombus

a parallelogram with 4 congruent sides

Square

all sides are the same and all angles are the same -- a regular quadrilateral

Trapezoid

a quadrilateral with exactly one pair of parallel sides

Circles and Their Terms

Circle

the set of all points equidistant from a central point

Radius

a segment from the center to any point on the circle

Diameter

the longest chord in a circle -- passes through the center of the circle

Circumference

the distance around a circle -- like a perimeter but for a circle

Chord

a line segment with both endpoints on the circle

Tangent

a line that intersects the circle at exactly one point

Pt. of Tangency

the point where a tangent and a circle meet

Concentric

concentric circles are circles that share the same center

Arc

the part of a circle between two points on the circle

Minor Arc

an arc of less than 180 degrees

Major Arc

an arc of more than 180 degrees

Semicircle

an arc of exactly 180 degrees

Central Angle

angle formed by segments from the end pts of the arc & the center of the circle

Common Polygons

Total of Interior Angles

Each Interior Angle (if Regular)

Total of Exterior Angles

Each Exterior Angle (if Regular)

Triangle

3-sided polygon

180

60

360

120

Quadrilateral

4-sided polygon

360

90

360

90

Pentagon

5-sided polygon

540

108

360

72

Hexagon

6-sided polygon

720

120

360

60

Heptagon

7-sided polygon

900

128.57

360

51.43

Octagon

8-sided polygon

1080

135

360

45

Nonagon

9-sided polygon

1260

140

360

40

Decagon

10-sided polygon

1440

144

360

36

Dodecagon

12-sided polygon

1800

150

360

30

Icosagon

20-sided polygon

3240

162

360

18

n-gon

an "n"-sided polygon

360

Special Quadrilateral

Parallel-

Isosceles

Kite

Rectangle

Square

Rhombus

Property

ogram

Trapezoid

Opposite sides are parallel

X

X

Opposites sides are congruent

X

X

Opposite angles are congruent

X

X

Diagonals bisect each other

X

X

Diagonals are perpendicular

X

X

X

Diagonals are congruent

X

X

X

Exactly one line of symmetry

X

X

X

X

Exactly two lines of symmetry

X

X

X

X

Logic Statements

Statement

If p, then q.

If two angles are congruent, then they have the same measure.

Converse

If q, then p.

If two angles have the same measure, then they are congruent.

Inverse

If not p, then not q.

If two angles are not congruent, then they do not have the same measure.

Contrapositive

If not q, then not p.

If two angles do not have the same measure, then they are not congruent.

Euler Line

The Orthocenter, Circumcenter, and the Centroid will always lie on the Euler Line. The Incenter will only be on the line in an Isosceles Triangle. In the case of the Equilateral Triangle all of the points come together to meet at exactly the same point.

Parallel Lines

Name

Property

Description

Example

Corresponding Angles

Congruent

angles in the same locations on the transversal & the parallel lines

2 & 6 (See Below)

Alternate Interior Angles

Congruent

angles on opposite sides of the transversal & inside the parallel lines

3 & 5 (See Below)

Alternate Exterior Angles

Congruent

angles on opposite sides of the transversal & outside the parallel lines

1 & 7 (See Below)

Same Side Interior Angles

Supplementary

angles on the same side of the transversal & inside the parallel lines

4 & 5 (See Below)

Same Side Exterior Angles

Supplementary

angles on the same side of the transversal & outside the parallel lines

1 & 8 (See Below)

Angle of Elevation and Angle of Depression

Geometry Definitions & Conjectures

Page 3 of 21

Parts of Circles

Coordinate Midpoint Property

If (x1, y1) and (x2, y2) are the coordinates for the endpoints of a segment, then the coordinates for the midpoints can be for the midpoints can be found using the following formula:

Slope

Slope-intercept form:

Where (x,y) are the coordinates for any point on the circle, m is the slope and b is the y-intercept (where the line crosses the y axis).

The slopes of parallel lines are the same.

The slopes of perpendicular lines are negative reciprocals of each other .

Triangle Congruence Shortcuts

Transformations

Isometry - A transformation that keeps the size and shape of geometric figures the same.

Translation is when we slide a figure in any direction.

Reflection is when we flip a figure over a line.

Rotation is when we rotate a figure a certain degree around a point.

Dilation is when we enlarge or reduce a figure.

Coordinate Transformations Conjecture

The