Question

I NEED THIS DONE, PLEASE SHOW ALL WORK!! PICTURE 1 IS FOR QUESTION 3 AND PICTURE 2 IS FOR QUESTION 2. THANK YOU

fill in the blanks in the following proof:

1. given: 4x=8(x-2)
prove: x = 4

statement — reason
1. 4x=8(x-2) — 1.
2. — 2. distributive property
3. -4x = -16 — 3.
4. x = 4 — 4.

2. write a paragraph for the following conjecture

given: m < SQR = 55°
m < PQS = 35°
prove: △PQR is a right triangle

3. write a paragraph proof, flowchart, or 2 column proof for the following

given: m < 1 = 27°, < 1 ^ < 2 are supplementary
prove: m < 2 = 153°

Answer 1

Answer:

See explanation

Step-by-step explanation:

Question 1. Write two-column proof.

       Statement                   Reason

1. $4x=8(x-2)$                    Given

2. $4x=8x-16$                   Distributive Property of Equality

3. $4x-8x=8x-8x-16\\ \\-4x=-16$ Subtraction Property of Equality

4. $x=4$                            Division Property of Equality

Question 2.

                   Statement                                 Reason

1. $m\angle SQR = 55^{\circ}$                           Given

2. $m\angle PQS = 35^{\circ}$                          Given

3. $m\angle SQR+m\angle PQS=m\angle PQR$  Angle Addition Postulate

4. $m\angle PQR=55^{\circ}+35^{\circ}\\ \\m\angle PQR=90^{\circ}$  Substitution Property of Equality

5. $\angle PQR$ is a right angle    Definition of a right angle

6. $\triangle PQR$ is a right triangle   Definition of a right triangle

Question 3:

                  Statement                                 Reason

1. $\angle 1$ and $\angle 2$ are supplementary                                 Given

2. $m\angle 1+m\angle 2=180^{\circ}$  Definition of supplementary angles

3. $m\angle 1=27^{\circ}$       Given

4. $27^{\circ}+m\angle 2=180^{\circ}$   Substitution Property of Equality

5. $27^{\circ}-27^{\circ}+m\angle 2=180^{\circ}-27^{\circ}\\ \\m\angle 2=153^{\circ}$   Subtraction Property of Equality