Download Acc. 10.1 Geometry.notebook

Acc. 10.1 Geometry.notebook
April 08, 2013
Do Now
Solve.
1. 15 = 2x - 7
3. a
16
=
2. 3 - 3n = 50
5
4
4. 90
15
=
x
34
Mar 22­5:10 PM
Geometry
A
A point indicates location. A point has no size. You
name a point by a capital letter.
point A
A line is a series of points that extend in two
opposite directions without end. You name a line by
any two points on the line, or a lower case letter.
n
A
B
AB, BA, n
A ray is a part of a line with one endpoint and all the
points of the line on one side of the endpoint. You
name a ray using two points, starting with the
endpoint.
A
A segment is part of a line with two endpoints and
all points in between. You name a segment by its
endpoints. AB indicates the length of AB.
A
B
AB, ray AB
B
AB, BA
Mar 21­3:54 PM
1
Acc. 10.1 Geometry.notebook
April 08, 2013
A plane is a flat surface that
extends indefinitely in all
directions and has no thickness.
Intersecting and parallel lines lie
in the same plane. Intersecting
lines have exactly one point in
common. Parallel lines are lines in
the same plane that never
intersect.
Skew lines lie in different planes.
They are neither parallel nor
intersecting.
planes
intersecting lines
parallel lines
skew lines
Mar 21­4:08 PM
An angle ( ) is formed by two
rays with a common endpoint.
You can call the angle at the
right DCE, ECD, C, or 1.
E
ra
y
1
D
ray
vertex
C
A vertex is the point of intersection of two sides
of an angle or figure. Point C is the vertex of the
angle at that point. The plural of vertex is
vertices.
You can use a protractor to measure angles.
Write "the measure of angle C" as m C.
Mar 21­4:16 PM
2
Acc. 10.1 Geometry.notebook
April 08, 2013
X
m X=
Mar 21­4:25 PM
You can classify angles by their measures.
acute angle
right angle
obtuse angle
between
0º and 90º
90º
between
90º and 180º
straight
angle
180º
Mar 21­4:27 PM
3
Acc. 10.1 Geometry.notebook
April 08, 2013
Working with pairs of angles
If the sum of the measures of two angles is 90º,
the angles are complementary.
If the sum is 180º, the angles are supplementary.
71º
65º
19º
complementary
115º
supplementary
Mar 21­4:33 PM
1
4
3
2
Adjacent angles share a vertex and a side but have no interior
points in common. Angles 1 and 2 are adjacent angles. Adjacent
angles formed by two intersecting lines are supplementary.
Angles 1 and 3 are vertical angles. Vertical angles are formed by
intersecting lines and are opposite each other. Vertical angles
have equal measures. Angles with equal measures are congruent
angles.
Mar 21­4:39 PM
4
Acc. 10.1 Geometry.notebook
April 08, 2013
Classifying Triangles
Congruent sides have the same length. You can classify a
triangle by the number of congruent sides it has.
scalene triangle
no congruent sides
isosceles triangle
at least 2
congruent sides
equilateral triangle
3 congruent sides
Mar 21­4:44 PM
You can also classify a triangle by its angle measure.
right triangle
one right angle
acute triangle
3 acute angles
obtuse triangle
1 obtuse angle
Mar 21­4:52 PM
5
Acc. 10.1 Geometry.notebook
April 08, 2013
• Cut out a paper triangle.
• Number the angles of the triangle
and tear them off the triangle.
• Place the three angles side by side
to form adjacent angles with no angles
overlapping.
1
3
2
• Make a conjecture about the sum of
the angle measures of your triangle.
The sum of the measures of the
angles of a triangle is
º.
Mar 21­4:56 PM
Mar 22­4:38 PM
6
Acc. 10.1 Geometry.notebook
April 08, 2013
Mar 22­4:42 PM
Mar 22­4:44 PM
7
Acc. 10.1 Geometry.notebook
April 08, 2013
Mar 22­4:47 PM
The perimeter of an equilateral triangle is 42 meters.
Find the length of each side.
Mar 22­4:49 PM
8
Acc. 10.1 Geometry.notebook
April 08, 2013
The perimeter of an isosceles triangle is 35 inches.
The length of the shortest side is 4 inches less
than the length of each of the other two sides.
Find the lengths of all three sides of the triangle.
Mar 22­4:50 PM
The ratio of the angle measures of a triangle is 1 : 3 : 5.
Find the angle measures. Then classify the triangle by
its angle measures.
Let xº, 3xº, and 5xº represent
Hint
the angle measures.
Mar 22­4:40 PM
9
Acc. 10.1 Geometry.notebook
April 08, 2013
The ratio of the angle measures of a triangle is 7 : 9 : 20.
Find the angle measures. Then classify the triangle by its
angle measures.
Mar 22­4:55 PM
If you know the measure of just one angle in a triangle,
what information do you need in order to find the
measures of the other angles?
either the relationship between the two unknown angle
measures, or the relationship between the known
measure and one of the two unknown measures.
Mar 22­4:56 PM
10