Transcript Geometry Proofs - About Mr. Chandler

Geometry Proofs
Obj: To Complete Proofs Involving
Segment Theorems
To complete proofs involving
angle theorems
5 Essential Parts to a Good
Proof
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State the theorem to be proved
List the given information
If possible draw a diagram to illustrate
the given information
State what is to be proved
Develop a system of deductive
reasoning
Deductive Reasoning
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Definitions & postulates-Statements
accepted as true w/o proof
Theorem- undefined terms that can be
used as truth once they have been
proven
Theorem:
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Congruence of segments is reflexive,
symmetric, and transitive
Written as symbols:
Reflexive: AB  AB
Symmetric: IF
AB  CD, then CD  AB
Transitive: IF
AB  CD and CD  EF
then AB  EF
Example:
D
C
Given:
B
ABCD
Prove: AD  AB  BC  CD
Statements
A
Justification
1.) ABCD
Given
1.) _________
2.) AD = AB + BD
Seg. + post
2.) ___________
3.) BD = BC + CD
Seg. + post.
3.)___________
4.) AD = AB + BC + CD
substitution
4.)___________
Your Turn:
P
Q
R
Given: pts PQRS are collinear
S
Prove: PQ = PS - QS
Statement
1.) pts PQRS are collinear
2.) PS = PQ + QS
3.) PS – QS = PQ
4.) PQ = PS - QS
Justification
Solution to “Your Turn”:
Given: pts PQRS are collinear
Prove: PQ = PS - QS
Statement
Justification
1.) pts PQRS are collinear
1.) Given
2.) PS = PQ + QS
2.) Seg. + post
3.) PS – QS = PQ
3.) Subtraction
4.) PQ = PS - QS
4.) symmetric Prop.
Verifying Angle Relationships
Theorems
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Supplement thm-if 2 angles form a
linear pr then they are supplementary
Congruence of angles is reflexive,
symmetric, and transitive
Angles supplementary to the same
angle or to congruent angles are
congruent
Theorems Continued
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Angles complementary to the same
angle or congruent angles are
congruent
All right angles are congruent
Vertical angles are congruent
Perpendicular lines intersect to form 4
right angles
Example:
If A and C are vertical ' s, and mA  3x  2
and mC  2 x  4 . Find mA& mC.
Angle A = Angle C, Vert. angles
3x - 2 = 2x + 4
-2x +2 -2x +2
x=6
A = 3(6) - 2
= 16o
C = 2 (6) + 4
= 16o
Your Turn:
Find the measure of each numbered angle
m1  2 x  5
m2  x  4
2x - 5 + x - 4 = 180
3x - 9 = 180
3x = 189
x = 63
1
2
m1  2 (63) - 5 = 121o
m 2  63 - 4 = 59o
Homework:
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Put this in your agenda:
Pg 116 5 – 12, 21 – 24
Pg 128 9 – 21 odd, 22 - 28