Review – Chapter 1

Essentials of Geometry

Ms. Rinaldi

Geometry

Points, Lines, and PlanesPoint – Indicates a location •A Point A

Line – A straight path that extends in opposite directions without end. Line m,

Plane – A flat surface that extends without end and has no thickness. Name by three capital letters or bold letter in corner.

Collinear Points – Points that lie on the same line.

Coplanar Points – Points that lie on the same plane.

Segment – A line that ends

Ray – A line that goes in one direction

Opposite Ray – Rays in opposite directions on the same line

Midpoint – The point that divides the segment into two congruent segments.

Segment Bisector – A point, ray, line, segment or plane that intersects the segment at its midpoint. (Cuts the segment in half)

AB

m

BAAB,

Identify Points, Lines, and Planes

a) Give 2 names for line m.

b) Name 3 collinear points.

c) Name a point not coplanar with V, S, and T.

d) Name the plane containing the points V, S, and T.

e) Name the intersection of line n and line m.

Opposite Rays

JE JFand are opposite rays.

Name another pair of opposite rays.

Segment Addition Postulate

a) Find AC.

b) Find AB if AC = 37.

A B C

13 7

A B C

11

Bisectors

J is the midpoint of XY. Find XJ if XY = 220.

The Midpoint Formula

The coordinates of the midpoint of a segment are the…

Find the midpoint of the segment with endpoints (-1, 8) and (7, -4)

2'

22121 yyxx

The Distance Formula

Find the distance between the points (3, 9) and (-2, 5)

212

212 )()( yyxx

Classifying Angles by their Measures

Acute Angle

Less than 90 degrees

Obtuse Angle

Greater than 90 degrees

Right Angle

90 degrees

Straight Angle

180 degrees

Angle Addition

Given that EFG is a right angle, find m EFH and m HFG.

Angle Pairs

Complementary Angles

2 angles who add up to 90 degrees

Supplementary Angles

2 angles who add up to 180 degrees

Adjacent Angles

2 angles who share a common vertex and side (Next to each other)

a. Given that 1 is a complement of 2 and m 1 = 68°, find m 2.

b. Given that 3 is a supplement of 4 and m 4 = 56°, find m 3.

More Angle Pairs

Linear Pair

2 adjacent angles whose noncommon sides are on the same line.

Add up to 180 degrees

Vertical Angles

2 nonadjacent angles whose sides are formed by 2 intersecting lines. (Like scissors)

These are congruent

Find the values of x and y.

2x°

(8x + 30)°

5y°

Polygons

Properties:-Plane figure (flat)-Closed-Straight sides-Doesn’t cross itself*A circle is not a polygon*

Convex – All corners point out

Concave – A corner “caves” in

Classifying Polygons by Sides

# of sides

Type of polygon

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

# of sides

Type of polygon

8 Octagon

9 Nonagon

10 Decagon

12 Dodecagon

n n-gon

Regular Polygons

Equilateral – All sides equal

Equiangular – All angles equal

Regular – Both

Classify the polygon by the number of sides. Tell whether it is concave or convex. Then, tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning.

a. b. c.

Regular Figures

The figure is a regular hexagon. Find the length of one of the sides.

5x – 7

2x + 2