Download 2C Drawing Logica Conclusions, part B

Introduction to Proof:
Drawing Conclusions, part 2b
Objectives:
To draw conclusions about angles
using given information
To use the substitution and
transitive properties
Mrs. McConaughy
GEOMETRY
1
Before we start, recall:
Measures are equal Parts are congruent
m BAC = m  DEF
 BAC   DEF
m AB = m CD
AB  CD
AB = CD
Mrs. McConaughy
GEOMETRY
2
If we know certain things about angles,
we can discover other things about them.
105
B
A
105
If m  A = 105 and m  B = 105,
m  A = m  B
then __________________________________.
If m
A = m
Mrs. McConaughy


 A   B
B, then ____________.
GEOMETRY
3
Example 1
If HJ bisects GHI, then ______________.
If  GHI   IHJ, then ________________.
J
I
G
Mrs. McConaughy
GEOMETRY
H
4
Drawing Conclusions
If  X   Y and  Y   Z,
then _______________________________.
If  X   Z, then
__________________________________.
Mrs. McConaughy
GEOMETRY
5
Transitive Property of
Congruence
If  X   Y and  Y   Z, then _____.
If AB  CD and CD  EF,___________.
Example 2
If  AOB   BOC and  BOC   COD,
which other angles are congruent?
Mrs. McConaughy
GEOMETRY
6
Substitution Property of
Equality
If m A = m  B, then A can be
substituted for B in any equation..
If AB = CD, then AB can be substituted
for CD in any equation.
Mrs. McConaughy
GEOMETRY
7
Example 3
Given m  T = 53 and m  V = 53, by the
substitution property, we can conclude
________________________________.
Therefore,
________________________________.
53
53
Mrs. McConaughy
T
GEOMETRY
V
8
Example 4
If GH = KL and KL = RT, then
__________________________.
You will use the transitive property and
substitution property in showing
relationships between angles or
segments.
Mrs.
McConaughy
GEOMETRY
9
Reading in Geometry
Completion. You may need to draw and
label diagrams to complete the
statements which follow. If necessary,
use the word bank below:
midpoint
conclusions
midpoint
Mrs. McConaughy
bisects
information
pictures
GEOMETRY
10
Geometry often involves using
information that is known to
discover other _______________.
This is called drawing __________.
For example, if you know that AB
_____  CAD, then you know that
 CAB   BAD.
Similarly, if P is the _________ of
AB, then you know that AP  PB.
Mrs. McConaughy
GEOMETRY
11
Homework Assignment
Drawing Conclusions WS
Mrs. McConaughy
GEOMETRY
12