Question

Given: Angles 1 and 4 are vertical angles.
Prove: Line l and m are congruent.

Answer 1

Please help me. It is an unscramble thing..

Answer 2

Statement:
<4 ≅ <5
line l ≅ line m
<1≅ <4
Angles 1 and 4 are vertical angles
<1≅ <5

Reasons:
Transitive Property
Given
Converse of Corresponding Angles Postulate
Alternate Interior Angles Theorem
Vertical Angle Theorem

Answer 3

1 and 4 are vertical angles. no need to be given. they are vertical angles by definition !

lines are congruent ? what do you mean.... you can prove two line-segments are congruent. but all lines are congruent by definition they are infinite

i am not getting the question :\

Answer 4

It wants you to fill it out as if it is a two column proof, and then switch it into another proof. The problem I have is that I am horrible are proofs, and cant figure out the order.

Answer 5

ok you start with Given

Answer 6

Angles 1 and 4 are vertical angles --- Given

Answer 7

Right, and I thought that would be the <1≅ <4 since that it what it said in the beginning

Answer 8

thats first row

Answer 9

Right.

Answer 10

<1≅ <4 --- Vertical Angle Theorem

Answer 11

your second row

Answer 12

okay.

Answer 13

<4 ≅ <5 --- Alternate Interior Angles Theorem

Answer 14

third row

Answer 15

angle 4 and angle 5 are alternate interior angles

Answer 16

right

Answer 17

<1≅ <5 --- Transitive Property

Answer 18

fourth row

Answer 19

and then line l ≅ m last.

Answer 20

line l ≅ line m ---- Converse of Corresponding Angles Postulate

Answer 21

yes we completed and its correct

Answer 22

but it is fully meaningless... i dont understand the phrase "congruent lines" itself :\

Answer 23

Thank you so much! And then if I wanted a paragraph proof, then it would just be explaining the steps?

Answer 24

its virtual math, they didnt go over this in the lesson at all, so im as confused as you are

Answer 25

yes just join the all rows with "and, so"
join columns with "since, because"

etc... :)

Answer 26

i am not confused. the phrase "congruent lines" is meaningless

Answer 27

Okay, thanks for the tips :) You just saved my butt

Answer 28

you can say "congruent line segments"

Answer 29

lol yw !(:

Answer 30

@rsadhvika sorry to keep asking questions, but how would I phrase ≅ in words?

Answer 31

congruent

Answer 32

thanks

Answer 33

its okay you can ask hundreds of questions. you're good :P

Answer 34

i have attached a snap that shows :
two-column proof, and its paragraph-proof version.

you can plagiarize the words from there ;)

Answer 35

http://www.mrperezonlinemathtutor.com/private2/GEOM_PDF_FILES/1_3_parragraph_proofs_intro.pdf

Answer 36

@rsadhvika THANKS!!!!!