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°