Honors Geometry

Proofs Involving Angles

Here are some suggestions that may help you when doing proofs.

1. Your given information (hypothesis) becomes your first statement. What you need to prove (conclusion) is your last

statement.

2. Reason backwards when possible.

3. Consider each piece of given information separately and make

any conclusion that follows.

4. In most proofs, you will have to write out at least one statement based on the figure. You may look for ONLY the following:

a)Angle Addition postulateb)Segment Addition Postulatec)Linear pairsd)Vertical Angles

5. In most proofs, you will use the Substitution Property shortly after the statement you make based on

the figure (usually within two steps). Watch for it!

Right Angle Theorem (RAT)

If _______________________

then_____________________

All right angles are congruent.

two angles are right angles

the angles are congruent.

Given: _______________Prove:_______________

1. 1.

2. 2.

3. 3.

A B

anglesright are B andA

BA

Given

90Bm 90,Am Def. of right angles

Substitution

anglesright are B and A

BA

Congruent Supplements Theorem

If two angles are supplements of the same or congruent angles, then they are congruent.

3 1

arysupplement are 4 and 3

arysupplement are 2 and 1 .1

Given .1

4 2

180 4m 3m

180 2m 1m 2.

supp. of Def. 2.

4m 3m 2m 1m 3. prop.on substituti 3.

4. propertyn subtractio 4.

Vertical angles are the nonadjacent angles formed when two lines intersect.

Vertical Angle Theorem (VAT):

12

34

Vertical angles are congruent.

1) 1) angles vert.are 2 and 1

21 )

Given

L.P. a are 3 and 2

L.P. a are 3 and 1 )2

L.P. of Def. 2)

supp. are 3 and 2

supp. are 3 and 1 )3

Post. P. L. 3)

Thrm. Supp. Cong. 4)4

arycomplement are 2 and 1 )1 Given )1

arycomplement are 2 and 3 )

90 2m 1m )2 Comp. of Def. )2

angles vert.are 3 & 1 )3 angles vert.of Def. )3

3 1 )4 theoremAngles Vert. )4

90 2m 3m )

Comp. of Def. )

onsubstituti )5