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3.8 Angle Proofs

Last updated about 1 month ago

7 Nsɛmmisa

6

3

6

8

5

6

13

Asemmisa {{asɛmmisaAhyɛnsode}}

1.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Def. of supplementary

m\angle B = m\angle E

\overline{DE}\perp\overline{EF}

Subtraction Prop.

Addition Prop.

Prove

Def. of bisect

Def. of \perp

Substitution prop.

Simplification

Def. of linear pair

Angle Addition Axiom

Multiplication Prop.

Given

Def. of complementary

m\angle E = 90^o

Division Prop.

Vertical Angles Thm.

m\angle B = 90^o

Asemmisa {{asɛmmisaAhyɛnsode}}

2.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Division Prop.

Subtraction Prop.

100^o

Angle Addition Axiom

Def. of \perp

180^0

90^o

Def. of linear pair

Def. of supplementary

Multiplication Prop.

Prove

Def. of bisect

Substitution prop.

Vertical Angles Thm.

Addition Prop.

Simplification

Given

Def. of complementary

Asemmisa {{asɛmmisaAhyɛnsode}}

3.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Vertical Angles Thm.

Subtraction Prop.

Def. of linear pair

Def. of bisect

m\angle 1 = m\angle 2

Substitution prop.

Def. of \perp

Simplification

Def. of supplementary

Def. of complementary

Angle Addition Axiom

Multiplication Prop.

Given

Prove

m\angle 2 = m\angle 3

\overline{AB}\perp\overline{BD}

m\angle 1 = m\angle 3

Division Prop.

Addition Prop.

Asemmisa {{asɛmmisaAhyɛnsode}}

4.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Division Prop.

Substitution prop.

Angle Addition Axiom

Def. of complementary

Vertical Angles Thm.

\angle 1\cong\angle 11

Def. of bisect

Multiplication Prop.

Def. of supplementary

\angle 1\cong\angle 9

Subtraction Prop.

\angle 9\cong\angle 11

Given

Addition Prop.

Prove

Simplification

Def. of linear pair

Def. of \perp

Asemmisa {{asɛmmisaAhyɛnsode}}

5.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Prove

Vertical Angles Thm.

\angle KHL\cong\angle LHM

Multiplication Prop.

Angle Addition Axiom

\angle KHL\cong\angle JHN

Simplification

\overline{HL} bisects \angle KHM

Def. of \perp

Subtraction Prop.

Substitution prop.

\angle KHJ\cong\angle KHM

Def. of linear pair

Def. of bisect

\angle KHJ\cong\angle NHM

Def. of supplementary

Division Prop.

Addition Prop.

Given

\angle LHM\cong\angle JHN

\angle KHM\cong\angle JHN

Def. of complementary

Asemmisa {{asɛmmisaAhyɛnsode}}

6.

Complete the proof. Read the statements carefully. That is part of this problem.

Mmuae Afoforo a Wobɛpaw:

Addition Prop.

\angle EFD\cong\angle CFB

Simplification

Def. of bisect

\overrightarrow{FC} bisects \angle EFC

Given

\angle CFB\cong\angle DFC

\overrightarrow{FC} bisects \angle DFB

Def. of \perp

Multiplication Prop.

Subtraction Prop.

Def. of supplementary

\overrightarrow{FD} bisects \angle DFB

Prove

Division Prop.

\overrightarrow{FD} bisects \angle EFC

\angle DFC \cong\angle EFD

\angle DFC\cong\angle DFC

Def. of linear pair

Angle Addition Axiom

Vertical Angles Thm.

Def. of complementary

Substitution prop.

Asemmisa {{asɛmmisaAhyɛnsode}}

7.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Def. of complementary

Def. of supplementary

Vertical Angles Thm.

Def. of \perp

\overline{IP} bisects \angle GIM

m\angle MIP = 45^o

m\angle MIG = 90^o

Simplification

Angle Addition Axiom

\overline{IG}\perp\overline{ML}

Def. of bisect

Addition Prop.

Prove

Multiplication Prop.

\angle PIG \cong \angle MIP

Def. of linear pair

m\angle MIP + m\angle MIP = 90^o

Given

Subtraction Prop.

Substitution prop.

Division Prop.