Mini Vocabulary Proofs
Unit 6 – Day 2
Vertical Angles – Never-Given-Given #1
Given: lines and intersect
Prove:
𝑛1
𝑚
2
Statement Reason
1) 1) Vertical ’s are
Mark the picture!!!
Q.E.D.
∠1≅∠2
Reflexive Sides – Never-Given-Given #2
Given: Triangle ABC with drawn
Prove:
Statement Reason
1) 1) Reflexive Property
Mark the picture!!!
Q.E.D.
𝐵𝐷≅ 𝐵𝐷
A
B
CD
Reflexive Angles – Never-Given-Given #3
Given: Triangle ABC with drawn
Prove:
Statement Reason
1) 1) Reflexive Property
Mark the picture!!! Q.E.D.
∠𝐵≅∠𝐵
A
B
C
D E
Supplements of SupplementsNever-Given-Given #4
Given:
Prove:
Statement Reason
1) 1)
2) 2)
3) 3)
Given
and are supplementary and are supplementary
Q.E.D.
Linear pairs aresupplementary
Supplements of ’s are
∠2≅∠3
1 2 3 4
Mark the picture now!!!
Mark the picture again!!!
Angle Bisector
Given: bisects
Prove:
A
B
C
D
bisects
Statement Reason
1) 1)
2) 2) ∠𝐴𝐵𝐷≅∠𝐶𝐵𝐷
Given
An bisectorcreates 2 ’s
definition
outcome
Mark the picture!!!
Q.E.D.
Midpoint
Given: is the midpoint of
Prove:
Statement Reason
1) 1)
2) 2) 𝐴𝑀 ≅ 𝐵𝑀
Given
A midpointcreates 2 segments
definition
is the midpointof
outcome
Mark the picture!!!
A M B
Q.E.D.
Median
Given: is the medianof
Prove:
Statement Reason
1) 1)
2) 2)
3) 3)𝐴𝑀 ≅ 𝐵𝑀
Given
A midpointcreates 2 segments
is the midpointof
outcome
Mark the picture!!!
Q.E.D.
outcome
definition
A B
C
M
is the medianof definition
A median createsa midpoint
Parallel Lines – Alternate Interior Angles
Given:
Prove:
Statement Reason
1) 1)
2) 2) ∠1≅∠2
Given
If 2 || lines are cut by atransversal, thenalternate interior’s are
Theorem
𝑚∨¿𝑛
outcome
Mark the picture!!!
12
𝒎
Q.E.D.
𝒏
𝒑
Parallel Lines – Corresponding Angles
Given:
Prove:
Statement Reason
1) 1)
2) 2) ∠3≅∠4
Given
If 2 || lines are cut by atransversal, thencorresponding’s are
Theorem
𝑚∨¿𝑛
outcome
Mark the picture!!!
34
𝒎
Q.E.D.
𝒏
𝒑
Isosceles Triangle - sides
Given:
Prove:
Statement Reason
1) 1)
2) 2) ∠𝐴≅∠𝐶
Given
In a , ’s opposite sides are
Theorem
𝐴𝐵≅𝐶𝐵
outcome
Mark the picture first!!!
Q.E.D.
A
B
CMark the
picture again!!!
Isosceles Triangle - Angles
Given:
Prove:
Statement Reason
1) 1)
2) 2) 𝐴𝐵≅𝐶𝐵
Given
In a , sides opposite ’s are
Theorem
∠𝐴≅∠𝐶
outcome
Mark the picture first!!!
Q.E.D.
A
B
CMark the
picture again!!!
Perpendicular Lines
Given:
Prove:
Statement Reason
1) 1)
2) 2)
3) 3)∠𝐶𝐸𝐴 ≅∠𝐷𝐸𝐴
Given
All right ’s are
and are right angles
outcomeMark the picture!!!
A E B
Q.E.D.
C
D
𝐶𝐷⊥𝐴𝐵definition
lines form right ’s outcome
Common sense
Altitude
Given: is the altitudeof
Prove:
Statement Reason
1) 1)
2) 2)
3) 3)
4) 4)∠1≅∠2
Given
All right ’s are
and are right angles
outcome
Mark the picture!!!
A
B
Q.E.D.
CD
𝐶𝐷⊥𝐴𝐵definition
lines form right ’s
outcomeCommon sense
is the altitudeof
An altitude forms lines
definition
outcome
1 2
Segment Bisector
Given: bisects
Prove:
Statement Reason
1) 1)
2) 2)
3) 3)𝐴𝑀 ≅ 𝐵𝑀
Given
A midpointcreates 2 segments
is the midpointof
outcomeMark the picture!!!
A M B
Q.E.D.
C
D
bisects definition
A segment bisectorcreates a midpoint
outcome
definition
Perpendicular Bisector
Given: is the bisectorof
Prove: and
Statement Reason
1) 1)
2) 2)
3) 3) a)
Given
a) All right ’s are
a) and are right angles
outcome B
Mark the picture!!!
A E B
Q.E.D.C
D
is the bisectorof definition
a) lines form right ’s
outcome A
definition
b) is the midpointof
b) A segment bisectorcreates a midpoint
b)
outcome B
Comm
on
sense
b) A midpointcreates 2 segments
outcome A
Complements of Complements
Given: and
Prove:
Statement Reason
1) 1)
2) 2)
3) 3)
4) 4)
5) 5)
6) 6)
∠𝐴𝐵𝐸≅∠𝐶𝐵𝐷
Given
All right ’s are
and are right angles
outcome
Mark the picture now!!!
A
E
B
Q.E.D.
C
D
𝐴𝐵⊥𝐵𝐸 lines form right ’s
outcomeCommon sense
definition
∠𝐷𝐵𝐸 ≅∠𝐷𝐵𝐸
∠ 𝐴𝐵𝐷≅∠𝐶𝐵𝐸
Reflexive
Complements of ’s are
Mark the picture again!!!
Last Time
& are complementary & are complementary
Complementary anglesadd up to 90°