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vladimir1956 [14]
3 years ago
8

Write a paragraph proof of Theorem 3-8: In a plane, if two lines are perpendicular to the same

Mathematics
2 answers:
I am Lyosha [343]3 years ago
7 0

Answer: this theorem is true.

Step-by-step explanation: this theorem is in fact true. perpendicular lines mean one line cuts through another line and forms 90 degree angles. if two lines were to cut through the same line, then both lines would have to be parallel to each other considering the definition of perpendicular lines. for example in the picture both lines are completely horizontal making them form 90 degree angles. if these lines did not form 90 degree angles then they would not be perpendicular and at some point would cross paths. however they are straight meaning they will never touch, hence the parallel line definition.

Stells [14]3 years ago
6 0

Answer:

Check it out the paragraph below

Step-by-step explanation:

1) 1st Statement: 1) \:Given: r\perp\: s,\: t\perp s\\ Reason: Given 2) 2nd Statement: \angle 4 \:and\: \angle 8\:are\:right\:angles Reason: Lines are perpendicular when form right angles by meeting another line. 3) 3rd Statement: \measuredangle 4 =90^{\circ}\:and\:\measuredangle 8=90^{\circ} Reason: Definition of Right Angles. 4) 4th Statement: \measuredangle 4\cong \measuredangle 8 Reason: Congruent angles have the same angle measure. 5) 5th Statement: r\parallel s Reason: If their corresponding angles are congruent, then their lines are parallel. (Corresponding Angles Theorem).

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James has a board that is 3/4 foot long. He wants to cut the board into pieces that are each 1/8 foot long
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Hi, I'm happy to help!

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When a number is next to parenthesis with no sign, it means we are using multiplication. We can change this expression to look like this, by changing all the numbers next to the parenthesis with no sign, to one with a multiplication sign.

8(5+t) - 2(t+1) 8(5 + t) - 2(t+1)=

8×(5+t) - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

We start with parenthesis and solve everything inside of those, but, because everything inside the parenthesis are unlike terms, we cannot combine them.

Next, We look for any exponents (x²). There are none in this equation.

We then look for multiplication or division. There is a lot of multiplication, so we start solving that from left to right.

8×(5+t) - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

40+8t - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

40+8t - 2×(t+1)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (2t+2)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (2t+2)× 8×(5 + t) - 2×(t+1)=

(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=

(40+8t) - (16t+16)×(5 + t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - 2×(t+1)=

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

Now, before we do anything else, we need to recheck the parenthesis, now that they have changed. We can further simplify the middle parenthesis by adding together like terms.

(40+8t) - (80t+16t²+80+16t) - (2t+2)=

(40+8t) - ((80t+16t)+16t²+80) - (2t+2)=

(40+8t) - (96t+16t²+80) - (2t+2)=

(40+8t) - (96t+16t²+80) - (2t+2)=

Now, we look for addition or subtraction of like terms. We can now remove the parenthesis, since everything inside of the last two parenthesis is negative, we turn it negative, as long as we only combine the like terms.

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Once we find like terms, we can rearrange the expression.

(40-80-2)+8t - 96t+16t² - 2t

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(-42)+8t - 96t-16t² - 2t

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(-42)+(-90t)-16t²

(-42)+(-90t)-16t²

This doesn't have any like terms, so we don't alter it.

(122)+(-90t)-16t²

We can now remove the parenthesis.

122-90t-16t²

Since there are no more like terms this is the furthest we can simplify. We can then rearrange the expression to be arranged completely correct.

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I hope this was helpful, keep learning! :D

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