Question

The figure below shows a straight line AB intersected by another straight line t.

Write a paragraph to prove that the measure of angle 1 is equal to the measure of angle 3.

Answer 1

@ganeshie8

Answer 2

use linear pair angles to prove this. put something, il give hand if u get stuck :)

Answer 3

start like this :-

\(\angle 1 + \angle 2 = 180\) since these two form linear pair angles of line AB. Also, \(\angle 2 + \angle 3 = 180 \) since these two from linear pair angels of line t. By transitive property of equality, \(\angle 1 + \angle 2 = \angle 2 + \angle 3\). ...

Answer 4

Okay, so the transitive property of equality is basically a = b and b = c, then a = c

Linear angles are supplementary, so I get that angle 1 + angle 2 = 180 degrees and so on

I'm a little confused on how this proves that angles 1 and 3 are equal though, unless because both \[\angle1 + \angle2 = 180\] and \[\angle2 + \angle3 = 180\] both have \[\angle2\] in the equation, which means \[\angle1 \] and \[\angle3\] are equal because they both equal 180 when added with \[\angle2\]

Answer 5

So, the explanation I'm a little unclear on. @ganeshie8

Answer 6

subtract \(\angle 2 \) both sides

Answer 7

angle 1 = 180

angle 3 = 180

Answer 8

... (paragraph proof continues )\(\angle 1 + \angle 2 = \angle 2 + \angle 3\) . By subtraction property of equality \(\angle 1 = \angle 3\)

Answer 9

we're done.

Answer 10

the reply you deleted was correct lol :)

Answer 11

Oh. I deleted it because I thought I should've added the =180. Thank you!

Answer 12

Flo told Eddy, “If a bird is an ostrich, then it cannot fly.”

Which statement is the contrapositive of the above statement?

If a bird can fly, then it is not an ostrich. ---> This is my answer

If a bird is not an ostrich, then it can fly.

If a bird cannot fly, then it is an ostrich.

If a bird is an ostrich, then it cannot fly.

@ganeshie8 is my answer correct?

Answer 13

Because the contrapositive of a statement negate both parts of the statement, and rearranges the order.

Answer 14

perfect ! you're very good :)

Answer 15

Jazz draws a transversal, t, on two parallel lines AB and CD, as shown below.

He makes the following table to prove that the alternate interior angles are equal.

Which is the missing justification?

a) Angles 1 and 3 are supplementary; therefore, angle 2 is equal to angle 4.

b) Angles 1 and 3 are congruent; therefore, angle 2 is equal to angle 4.

c) Angles 1 and 4 and angles 1 and 2 are supplementary; therefore, angle 2 is equal to angle 4.

d) Angles 1 and 4 and angles 1 and 2 are congruent; therefore, angle 2 is equal to angle 4.

@ganeshie8

Answer 16

look at this :-
c) Angles 1 and 4 and angles 1 and 2 are supplementary; therefore, angle 2 is equal to angle 4.

Answer 17

That makes sense, it' similar to the question you just helped me solve!

Answer 18

Nathan, Joshua, Michelle, and Denise were in a room where a porcelain vase was found broken. When an inquiry was conducted by the building caretaker, each made a statement.

Nathan: I did not break the vase.
Joshua: Denise did it.
Michelle: Denise lied when she said Michelle did it.
Denise: Michelle did it.

The caretaker knew that only one statement is not true and concluded that Nathan broke the vase.

Describe in complete sentences the method you use to show that the caretaker made an incorrect conclusion.

{I'm kind of stick on this one}

Answer 19

Joshua blames Denise, Denise blames Michelle, Michelle concludes that Denise is lying, and Nathan says he didn't break it.

Answer 20

So, from the given information, the caretaker make an incorrect conclusion - meaning Nathan obviously wasn't lying and didn't do it. Joshua blames Denise, and Michelle concludes that Denise's statement is a lie. So, I think the person who broke the vase was Denise.

Answer 21

I just am unsure of how to explain that correctly, and I don't know what the question is asking when it says "method"

Answer 22

you need to use "indirect proof"

Answer 23

post it as a new question, il let somebody else help u wid this...