Angles and Their Measures
A
Angle the union of 2 rays that have the same endpoint
Sides of an Angle 2 rays that form the angle
uuu
r
uur
u
Example: BA and BC
B
C
Vertex common endpoints of 2 rays
X
Notation
XWY or
YWZ or
XWZ
Y
1
2
1
2
Z
W
Zero Angle an
Unions and Intersections of Figures
Union set of all elements in a set A, a set B, or both
A B A or B
Intersections set of elements in both A and in B
A B A and B
If there are no points in common then it is a null set or empty set.
cfw_
Examples:
2 Sets
2
Notes- The Triangle Inequality
Recall: A postulate is a statement we assume to be true.
Triangle Inequality Postulate The sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
This means that for any triangle ABC,
If Then Statements
Conditional a sentence with and if clause and a then clause
Antecedent (hypothesis) The clause following the if
Consequent (conclusion) the clause following the then
Example:
If it is Thursday, then were having pizza for dinner
Antecede
POLYGONS Notes
The book describes a triangle as a union of three segments.
What is wrong with this definition? (Show counterexample below.)
- not accurate
*We need:
3 segments to intersect
Intersections to be endpoints
Polygon The union of segments in the
Distance between Points
A number is between two others if it is greater than one of them and
less than other.
A point is between two others if it is collinear and its
coordinates are between its coordinates.
How many points can be between any two points?
The Need for Good Definitions
What makes a good definition?
1. includes words commonly understood, defined earlier, or purposely undefined
2. accurately describes the idea being defined
3. included no more information then necessary
Example 1
Midpoint the
Convex- The Need for Definitions
Convex Set a set in which every segment that connects points of a set lies entirely in
the set
Convex
Convex
Convex
Non-Convex
Non-Convex
Conjectures
Review:
Conditional If Then statement p q
Converse If Then statement q p
Define conjecture: An educational guess or opinion
Specific conjecture conjecture made with reference to a particular situation
Ex.
The area of that square is 4.
That boy
Converses
Converses Switch antecedent and consequent
Original conditional p q
Converse q p
*converses can be true or false
TRUE conditionals
1. If I leave Nebraska, then Ive crossed a state border.
(p)
(q)
p q True
q p False (you could cross the border of
Arcs & Rotations
Refer to Circle O.
B
A
O is the center of the circle
From A to B on the circle is
an arc
AB (arc AB)
The measure of is measured in degrees
AB
and is the same as the mAOB .
Note: The measure of an arc is not the same as
the length of the
NAME_
STUDENT ID #_
MRS. CARTER / MRS. PIRONE / MS. WATSON
Honors Geometry Summer Packet
NHHS and VHS
This summer packet is for all students enrolled in Honors Geometry for 2016-2017 school
year. The entire packet will be due and collected on the first FR