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Copy everything shown and write a two-column proof.
Given: mDBA=45; mDEB=45.

Prove:DBCFEB

Short Answer

Expert verified

The two column proof is:

Statements

Reasons

mDBA=45,mDEB=45

Given

DBA+DBC=180

Definition of supplementary angles

DBC=135

By solving the equation DBA+DBC=180.

DEB+FEB=180

Definition of supplementary angles

FEB=135

By solving the equationDEB+FEB=180

DBCFEB

As, DBC=135,FEB=135

Step by step solution

01

Step 1. Observe the given diagram.

The given diagram is:

02

Step 2. Description of step.

It is being given thatmDBA=45 and mDEB=45.

From the diagram it can be noticed that the anglesDBA andDBC forms the linear pair.

Therefore, the sum of the anglesDBA andDBC is 180.

That implies, DBA+DBC=180.

Therefore, it can be obtained that:

DBA+DBC=18045+DBC=180DBC=18045DBC=135

Therefore, the measure of the angleDBC is 135.

From the diagram, it can be noticed that the anglesDEB andFEB forms the linear pair.

Therefore, the sum of the anglesDEB andFEB is 180.

That implies, DEB+FEB=180.

Therefore, it can be obtained that:

DEB+FEB=18045+FEB=180FEB=18045FEB=135

Therefore, the measure of the angleFEB is 135.

As, DBC=FEB=135, therefore DBCFEB.

Hence proved.

03

Step 3. Write the two column-proof.

The two column proof is:

Statements

Reasons

mDBA=45,mDEB=45

Given

DBA+DBC=180

Definition of supplementary angles

DBC=135

By solving the equation DBA+DBC=180.

DEB+FEB=180

Definition of supplementary angles

FEB=135

By solving the equationDEB+FEB=180

DBCFEB

As, DBC=135,FEB=135

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