geometric proofs
DESCRIPTION
This slideshow helps introduce geometric proofs. It gives key elements and types of reasons then gives several different types of proofs. Toward the end of the slideshow- the two column proof's statements and reasons are scrambled and the students are responsible for unscrambling the proof. There are also some fill in the blank for students to complete.TRANSCRIPT
Geometric Proofs
27 October 2009
Geometric Proofs
TWO COLUMN PROOFS
FIVE KEY ELEMENTS 1. Given
2. Diagrams3. Prove
4. Statements5. Reasons
ReasonsGiven Information
DefinitionsPostulates
PROPERTIESTheorems
Given: ary.supplement are 3 and 2
and ary,supplement are 2 and 1
PROVE: 31 STATEMENTS Reasons 1.
ary.supplement are 3 and 2
and ary,supplement are 2 and 1
1. Given
2.
18032
18021
mm
mm 2. Definition of supplementary angles
3. 3221 mmmm 3. Substitution Property
4. 31 mm 4. Subtraction Property
5. 31 5. Definition of Congruent Angles
Given: 32 angle.right a is BAC
Prove: ary.complement are 3 and 1
B
A C
12
3
Statements Reasons
1.
2.
3.
4.
5.
6.
7.
8.
1.
2.
3.
4.
5.
6.
7.
8.
angle.right a is BAC Given
90BACm Definition of Right Angle
BACmmm 21 Angle Addition Postulate
9021 mm Substitution Property (Steps 2 and 3)
32 Given
32 mm Definition of Congruent Angles
9031 mm Substitution Property (Step 4 and 6)
ary.complement are 3 and 1 Definitions of Complementary Angles
Given:
Prove:
45XBCm and ABC bisects BX
angleright a is ABC
A
B C
X
45˚
QUIZ
• What is always the first step of a proof?• Name 5 key elements of a proof.• Name 5 types of reasons one can use during a
proof.• Measures __________: Angles and Segments
are ______________.• What is the last statement in a proof?
Statements Reasons1.
2.
3.
4.
5.
6.
7.
8.
9.
1.
2.
3.
4.
5.
6.
7.
8.
9.
ABC bisects BX Given
XBCABX
XBCmABXm
45XBCm
45ABXm
ABCmXBCmABXm
ABCm 4545
angle.right a is ABC
ABCm90
Definitions of Angle Bisector
Definitions of Congruent Angles
Given
Substitution Property
Angle Addition Postulate
Substitution Property
Simplify
Definition of Right Angle
Given:
Prove:
EBDABC
EA
.AE ofmidpoint theis B
EBDABC
A EB
C D
Statements Reasons
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
EA EBDABC
.AE ofmidpoint theis B
EBAB
EBDABC
Given
Given
Given
Definition of Midpoint
ASA (Steps 1, 4, 2)
Given: , 1 2 180AB BC m m #$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$ $#$
Prove: BC CD#$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$ $#$
A
B C
D
2
1
Statements Reasons
BC CD#$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$ $#$
1 and 2 are supplementary.
1 2 180m m
AB BC#$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$$#$ $#$
Converse of the Consecutive Interior Angles Theorem
Given
Definition of Supplementary Angles
Perpendicular Transversal Theorem
Given
CD toparallel is AB
Given:
Prove:
A
B D
EC
1 2 3 4
DEBC parallel is
43 ,21 ,CD toparallel is AB
Statements Reasons
CD toparallel is AB
31 43 ,21
23 ,41
DEBC toparallel is Given
Corresponding Angles Postulate
Substitution Property
Given
Converse of Corresponding Angles Postulate
42
Substitution Property
1.1.
2.2.
3.
3.
4.
4.5.
5.6.
6.
Given: WY XZProve: WX YZ
W
X
Y
Z
Statements Reasons
1.
2.
3.
4.
5.
WX XY
WY XZ
WY
XY YZ
1.
2.
3.
4.
5.
Segment Addition Postulate
Substitution Property
Given:
Prove:
is a right angle.LON
4 and 5 are complementary.
L
O N
M
45
Statements Reasons
1.
2.
3.
4.
5.
6.
1.
2.
3.
4.
5.
6.
is a right angleLON
m LON
LON
Definition of Right Angle
Substitution Property
m m m
m m
