Question

Complete the two-column proof.
Given: ∠2 and ∠5 are supplementary
Prove: l is parallel to m

Answer 1

@terenzreignz

Answer 2

lol why tag me of all people XD

And I don't get it, is that an answer box on the bottom?

Answer 3

thats my answer but i'm not sure

Answer 4

I see.
Let me just say that we may have been taught different ways on completing two-column proofs.

Now, 'given' is never a statement, always a 'reason'

The statement corresponding to it is THE given statement, which is?

Answer 5

<2 and <5 ?

Answer 6

Write the entire given statement.
Or shorten it, just make sure you don't change the meaning.

Answer 7

@terenzreignz help me with a few more after this <3 pls

write a paragraph proof of this theorem: In a plan, if two lines are perpendicular to the same line, then they are parallel to each other.

Answer 8

So the statement would be <2 and <5 are supplementary and reason is given?

Answer 9

yup.

Answer 10

So everything else is right even both 4s?

Answer 11

3 is a bit off.

Answer 12

I'm thinking...

Answer 13

What would it be then? since supplementary = 180

Answer 14

Yeah, but that's the definition of supplementary, not the reason that those two are supplementary...
Unless I'm mistaken, it's because of substitution.

I need a second opinion here...
@ganeshie8 ?

Answer 15

"By substitution" looks good to me for statement3's reason

Answer 16

the problem here is that they only gave the student four lines to prove it, which means skipping a few major steps...

Answer 17

1. \(\angle 2 \) and \(\angle 5\) are supplementary 1. Given
2. \(\angle 3 \cong \angle 2\) 2. By vertical angles theorem
3. \(\angle 3\) and \(\angle 5\) are supplementary 3. By substitution
4. \(l || m\) 4. By converse of same side interior angles theorem

Answer 18

we can conclude it short by using that theorem/postulate...

Answer 19

that sounds right what about my second question

Answer 20

Seems simple enough, and good thing it's a paragraph proof and not a bloody two-column one :D

Answer 21

Are you allowed to use that illustration?

Answer 22

yes

Answer 23

Well then, start with the statement that suppose r and t are parallel to line s.

Answer 24

err perpendicular, not parallel :D

Answer 25

@tyr1
pay attention >:(

;)

Answer 26

i have 2 more questions for you after this ,_,

Answer 27

1. What is the slope of the line shown
2. Find the values of x,y, and z The diagram is not to scale

Answer 28

so on 2 . X = 117 or 81? i'm not sure

Answer 29

@terenzreignz @ganeshie8 pls friends <:

Answer 30

you're done wid that perpendicular lines question (2nd) ?

Answer 31

yea

Answer 32

can u show me what u got for that proof ?

Answer 33

On the question before?

Answer 34

If r is perpendicular to s, then by the definition of perpendicular lines angle 4 has a measure of 90 degrees. Using the same logic with line t, angle 6 is 90 degrees. Since the same side interior angles are supplementary, line r is parallel to line t.

Answer 35

looks good, let me change it a bit, real quick

Answer 36

If r is perpendicular to s, then by the definition of perpendicular lines angle 4 has a measure of 90 degrees. Using the same logic with line t, angle 6 is 90 degrees. Since the same side interior angles are supplementary, line r is parallel to line t by converse of same side interior angle theorem.

Answer 37

okay

Answer 38

paragraph proof and two column proofs should contain same info

Answer 39

in two columnn proof, u divide statements/reasons in two columns

Answer 40

in paragraph proof u mix everything.
u must give proper justifications for everything u use/say ok

Answer 41

ok

Answer 42

1. What is the slope of the line shown

Answer 43

u knw slope formula ?

Answer 44

yea y2 - y1 x2 - x1 right?

Answer 45

y2-y1
--------
x2-x1

Answer 46

look at the given graph,
do u see two points on the line ?

Answer 47

okay i think i can do that one give me a second

Answer 48

okie

Answer 49

-4 + 9 5
5 - -2 3

Answer 50

nope, try agian

Answer 51

Did i mix the points up

Answer 52

(-2, 5) and (9, -4)

Answer 53

(-2, 5) and (9, -4)
x1 y1 x2 y2

Answer 54

-4 + 5 1
9 - -2 7

Answer 55

or do i add both and get -9 over 11

Answer 56

slope = \(\large \frac{y_2 - y_1}{x_2 - x_1}\)

Answer 57

\(\large \frac{-4-5}{9--2} = \frac{-9}{11}\)

Answer 58

what about #2?

Answer 59

use below :-

interior angles in a triangle add up to 180

Answer 60

\(\large 63 + 36 + x = 180\)

Answer 61

solve \(x\)

Answer 62

so x is 81 what about the z and y thats my problem

Answer 63

yes

Answer 64

look at the given pic,
\(\angle x\) and \(\angle z\) are linear pair angles right ?