P 1. What is the reason for step 3 in the two-column proof?

Given: ¿PQR is a right angle

Prove: _PQS and 2SQR are complementary

R

STATEMENTS

REASONS

1. ZPQR is a right angle

1. Given

2. MLPQR = 90°

2. Definition of Right Angle

3. m2PQS + m2SQR = MLPQR

3. ?

4. MzPQS + MzSQR = 90°

4. Substitution Property of Equality

5. ZPQS and SQR are complementary 5. Definition of Complementary Angles

А

Definition of Congruent Angles

B

Vertical Angles Congruence Theorem

с

Angle Addition Postulate

D

Definition of Angle Bisector

[tex]P 1. What is the reason for step 3 in the two-column proof? Given: ¿PQR is a right angle Prove: _[/tex]

Refer to the attached image.

Given:

The measure of [tex]\angle JMK= 52^\circ[/tex] and [tex]\angle KML= 38^\circ[/tex].

Also, Three rays ML, MK, and MJ share an endpoint M. Ray MK forms a bisector as shown in the attached image and the bisector divides angle JML into two parts.

To Prove: [tex]\angle JML[/tex] is a right angle.

Proof:

Statements Reasons

1. [tex]m \angle JMK=52^\circ[/tex] Given

2. [tex]m \angle KML=38^\circ[/tex] Given

3. [tex]m \angle JMK+m \angle KML=m \angle JML[/tex]

The reason for statement 3 is Angle addition postulate. As angle JML is composed of 2 angles that is angle JMK and angle KML. So by adding the measures of angles JMK and KML, we will get the measure of angle JML which is referred as Angle addition postulate.

4. [tex]52^\circ+38^\circ = m \angle JML[/tex] Substitution property of equality

5. [tex]90^\circ = m \angle JML[/tex] Simplification

6. [tex]\angle[/tex]JML is a right angle. Definition of right angle

[tex]What is the reason for statement 3 of the two-column proof? angle addition postulate definition of[/tex]

1. ∠1 is complementary to ∠2. 1. givem

2. m∠1 + m∠2. 2. Definition of complementary

3.BD bisects ∠ADC. 3. Given

4. 4. Definition of bisect

5. m∠2 = m∠3 5.

6. m∠1 + m∠3 = 90° 6. sunsitution

7. 7.

1. given

2. measure angle 1 plus measure angle 2 equals 90 degrees

3. B D bisects angle A D C

4. definition of angle bisector

5. definition of congruence

6. measure angle 1 is equal to measure angle 3

7. angle 1 is congruent to angle 3

7. definition of congruence

hope that helps

1. Angle addition postulate (this could be wrong)

2. Definition of bisect

3. Definition and postulate

4. Screenshot at the bottom

Last one I can't help, my bad.

[tex]1. what is the reason for statement 3 of the two-column proof? angle addition postulate linear pair[/tex]

#1) Angle Addition Postulate; #2) Definition of bisect; #3) postulate, definition and conjecture; #4) Given, Segment Addition Postulate, Subtraction Property of Equality; #5) Angle Addition Postulate, 60°+40°=m∠ABC, 100°=m∠ABC, Definition of obtuse angle.

Step-by-step explanation:

The angle addition postulate says that when two angles have a common vertex and common side, the measures of the smaller two angles added together is equal to the measure of the larger angle formed by the two. In Statement 3 of Problem 1, JMK and KML are added to form JML. This is the angle addition postulate.

When a segment or a line bisects an angle, it cuts it into two equivalent angles. This is why the angles formed by bisector PQ, RPQ and QPS, are congruent.

Postulates, definitions, conjectures and theorems can all be used as reasons in a two-column proof. Premises are not.

In #4, we are given that KL = MN. LN is formed by pieces LM and MN; this is the segment addition postulate. Once we have KL+LM = LM+MN, we can subtract LM from both sides; the property that allows us to do this is the subtraction property of equality.

In #5, we see that ∠ABC is formed by angles ABD and DBC; this is the angle addition postulate. ABC = 60° and DBC = 40°; we substitute these in for the angles, using the substitution property. We can then add these two angles together for a measure of 100°. This is by definition an obtuse angle.

Given below

Step-by-step explanation:

1. ∠1 is complementary to ∠2. 1.Given

2. m∠1 + m∠2.=90 degrees 2. Definition of complementary

3.BD bisects ∠ADC. 3. Given

4. Angle ADB = angle BDC 4. Definition of bisect

5. m∠2 = m∠3 5. Definition of bisect

6. m∠1 + m∠3 = 90° 6. substitution

7. Sums add up to 90 degrees. 7. angle 1 is complementary to angle 3.