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

See explanation

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