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Copy of 3.8 Angle Proofs (10/2/2025)

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 linear pair

Addition Prop.

Substitution prop.

Simplification

Subtraction Prop.

Angle Addition Axiom

m\angle B = m\angle E

Def. of \perp

Def. of bisect

Given

Def. of supplementary

Multiplication Prop.

Def. of complementary

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

Prove

Division Prop.

m\angle B = 90^o

m\angle E = 90^o

Vertical Angles Thm.

Asemmisa {{asɛmmisaAhyɛnsode}}

2.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Subtraction Prop.

Angle Addition Axiom

100^o

Def. of linear pair

Def. of \perp

Def. of bisect

Division Prop.

180^0

Substitution prop.

Multiplication Prop.

90^o

Vertical Angles Thm.

Def. of supplementary

Given

Simplification

Prove

Def. of complementary

Addition Prop.

Asemmisa {{asɛmmisaAhyɛnsode}}

3.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Def. of linear pair

Def. of \perp

Def. of complementary

m\angle 2 = m\angle 3

Simplification

Multiplication Prop.

Def. of bisect

Def. of supplementary

Angle Addition Axiom

Given

Substitution prop.

m\angle 1 = m\angle 2

Division Prop.

Subtraction Prop.

Addition Prop.

m\angle 1 = m\angle 3

Vertical Angles Thm.

Prove

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

Asemmisa {{asɛmmisaAhyɛnsode}}

4.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Given

Substitution prop.

Def. of bisect

\angle 9\cong\angle 11

Prove

\angle 1\cong\angle 11

Simplification

Def. of supplementary

Def. of linear pair

Def. of \perp

Vertical Angles Thm.

Subtraction Prop.

Division Prop.

Angle Addition Axiom

Multiplication Prop.

Addition Prop.

Def. of complementary

\angle 1\cong\angle 9

Asemmisa {{asɛmmisaAhyɛnsode}}

5.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

\angle KHJ\cong\angle KHM

Given

\angle KHJ\cong\angle NHM

Vertical Angles Thm.

Def. of complementary

\overline{HL} bisects \angle KHM

Addition Prop.

Multiplication Prop.

\angle KHL\cong\angle LHM

Angle Addition Axiom

Def. of \perp

Def. of supplementary

Subtraction Prop.

Def. of bisect

Division Prop.

Substitution prop.

\angle KHM\cong\angle JHN

Prove

Simplification

\angle KHL\cong\angle JHN

Def. of linear pair

\angle LHM\cong\angle JHN

Asemmisa {{asɛmmisaAhyɛnsode}}

6.

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

Mmuae Afoforo a Wobɛpaw:

\angle EFD\cong\angle CFB

Division Prop.

Def. of supplementary

\angle DFC\cong\angle DFC

Given

Def. of linear pair

Angle Addition Axiom

Prove

\overrightarrow{FC} bisects \angle DFB

Vertical Angles Thm.

Subtraction Prop.

\overrightarrow{FD} bisects \angle DFB

Multiplication Prop.

\overrightarrow{FC} bisects \angle EFC

\angle DFC \cong\angle EFD

Def. of complementary

\angle CFB\cong\angle DFC

Addition Prop.

Def. of \perp

\overrightarrow{FD} bisects \angle EFC

Substitution prop.

Simplification

Def. of bisect

Asemmisa {{asɛmmisaAhyɛnsode}}

7.

Complete the proof.

Mmuae Afoforo a Wobɛpaw:

Addition Prop.

Vertical Angles Thm.

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

Def. of \perp

Simplification

m\angle MIG = 90^o

Def. of linear pair

Angle Addition Axiom

m\angle MIP = 45^o

Subtraction Prop.

Prove

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

\overline{IP} bisects \angle GIM

Def. of supplementary

Given

\angle PIG \cong \angle MIP

Def. of complementary

Multiplication Prop.

Substitution prop.

Def. of bisect

Division Prop.