Section 1.2 Use Segments and Congruence
o Rules in geometry that are accepted without proofs
are called Axioms or postulates.
Postulate 1: Ruler postulate
- Points on a line can be matched up with real
numbers. These real numbers are coordinates of the
po
The Distance Formula
If A (x1 , y1 ) and B(x 2 , y2 ) are points
in the coordinate plane, then the distance
between A and B is (x 2 x1 ) 2 + (y 2 y1 ) 2
Example:
Use the Distance Formula. You
may find it helpful to draw a
diagram.
Example:
What is the app
Section 1.3 Use Midpoint and Distance
Formulas
The midpoint of a segment is the point
that divides the segment into two
congruent segments.
A segment bisector is a point, ray, line,
line segment, or plane that intersects the
segment at its midpoint.
A m
Section 1.4 Measure and Classify Angles
.
An _ consists of two
different rays with the same endpoint
The rays are the _of the angle.
The endpoint is the _ of the
angle
Example: Name three angles in the
diagram
Example: Name three angles in the
diagram
Cla
Section 2.2 Analyze Conditional Statements
A conditional statement is a logical
statement that has two parts, a hypothesis
and a conclusion
Conditional statements can be written in
If-then form
The if part contains the hypothesis and
the then part conta
Section 2.4 Use Postulates and Diagrams
More Postulates:
Postulate 5: Through any two points there exists exactly
one line.
Postulate 6: A line contains at least two points
Postulate 7: If two lines intersect, then their intersection
is exactly one point.
Section 2.3 Apply Deductive Reasoning
Deductive reasoning, uses facts,
definitions, accepted properties, and the
laws of logic to form a logical argument.
It differs from inductive reasoning, which
uses examples and patterns to make a
conjecture
Laws Of
Section 2.5 Reason Using Properties from Algebra
Algebraic Properties of Equality:
Let a, b, and c, be real numbers.
Addition property:
If a = b, then a + c = b + c
Subtraction property: If a =b, then a c= b-c
Multiplication prop:
If a = b, then ac = bc
D
Section 2.6 Prove Statements about Segments
and Angles
What is a proof?
A proof is a logical argument that shows a
statement is true
A two column proof has numbered statement and
corresponding reasons that show an argument in a
logical order
Write a two-c
Section 2.7 Prove Angle Pair Relationships
Theorem 2.3 Right Angles Congruence Theorem
All Right angles are congruent
Proof
Given: 1 and 2
Prove: 1 2
Statements
Reasons
1) 1 and 2 are right angles
1) Given
2) m1=90o , m2=90o
3)m1= m2
2) Definition of righ
Section 4.6 Use Congruent Triangles
Explain how you can use
the given information to
prove that the hanglider
parts are congruent.
GIVE
N
PROV
E
1
QT
RTQ
2,
RTS
ST
Use the give information to prove the parts of the
kite are congruent
Given: GK bisects FGH
Chapter 5 Vocabulary
Median
Point of Concurrency
Centroid
Angle bisector
Incenter
Perpendicular bisector
Concurrency of perpendicular bisectors
Isosceles Triangle
Base angles theorem
Triangle Inequalties
Possible side lengths for a triangle?
Hinge theorem
Section 4.5
Prove by ASA and AAS
Postulate 21: Angle Side- Angle (ASA)
Congruence:
If two angles and the include side of one
triangle are congruent to two angles and the
included side of a second triangle, then the
two triangles are congruent.
If:
Angle A
Section 10.6
Theorem 10.14
1) Construct a circle using a compass
2) Draw two chords in the circle using your ruler
3) Measure each individual piece of the chords. Label your measurements.
4) Multiply piece of chord one, by the second piece of chord one. T
Section 9.2 Matrices
To add or subtract matrices, you add or subtract
corresponding elements
Matrices have to have the same dimension to add or
subtract
BA
AC
Section 9.1 Transformations and Vectors
Transformations move or change figures.
Image the new figure created after a transformation
Pre-image is our original image that gets modified
Graph quadrilateral ABCD with vertices A(1, 2), B(1, 5), C(4, 6), and D(