Post on 05-Jan-2016
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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