Angles and Their Measures
Angle the union of 2 rays that have the same endpoint
Sides of an Angle 2 rays that form the angle
Example: BA and BC
Vertex common endpoints of 2 rays
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.
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
If it is Thursday, then were having pizza for dinner
The book describes a triangle as a union of three segments.
What is wrong with this definition? (Show counterexample below.)
- not accurate
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
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
The area of that square is 4.
Converses Switch antecedent and consequent
Original conditional p q
Converse q p
*converses can be true or false
1. If I leave Nebraska, then Ive crossed a state border.
p q True
q p False (you could cross the border of
Arcs & Rotations
Refer to Circle O.
O is the center of the circle
From A to B on the circle is
AB (arc AB)
The measure of is measured in degrees
and is the same as the mAOB .
Note: The measure of an arc is not the same as
the length of the
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