Question

Could someone explain this to me? I'll fan and medal.
Match the reasons with the statements given in the proof.
Given:
WX > XY
Prove:
1 > 4


Exterior ∠ = sum of remote interior ∠'s
Transitive property
If a = b + c and c>0, then a>b.
Given
Angle opposite longer side is larger angle.


WX > XY
∠3 > ∠4
∠1 = ∠3 + ∠2
∠1>∠3
∠1 > ∠4

Answer 1

which step doesn't make sense? We'll start from there and work down the line

Answer 2

I can't remember what the transitive property is. I know that WX > XY is the given and I know that ∠1 = ∠3 + ∠2 is Exterior ∠ = sum of remote interior ∠'s

Answer 3

the transitive property is the idea that if

a = b and b = c, then a = c

so it's like a connection from a to b to c

think of it as a car in transit going from point A to point B to point C

Answer 4

Oh okay, yes I remember that now. So would that be ∠1 > ∠4?

Answer 5

yes

you can also use the transitive property with inequalities too

here's how

let's say we know x > y and y > z

then certainly x > z too because x is larger than y

----------------------------

In your case, when you go from `∠1>∠3` to `∠1>∠4` you are using the transitive property of inequalities (since `∠3 > ∠4` is shown in step 2)

Answer 6

In a real life example you could have this

"If Alex is taller than Billy, and Billy is taller than Charlie, then Alex is also taller than Charlie"

That sentence translates to

if a > b and b > c then a > c

Answer 7

Ohhh okay I get it now. Would ∠1>∠3 be Angle opposite longer side is larger angle?

Answer 8

no `Angle opposite longer side is larger angle` is paired with `∠3 > ∠4`

angle 3 is opposite WX
angle 4 is opposite XY
since WX > XY this means angle 3 is larger than angle 4
WX is the larger side so angle 3 is the larger angle

this is the hinge theorem

http://ceemrr.com/Geometry1/HingeTheorem/paste_image2.gif

Answer 9

The reasoning for `∠1>∠3` is `If a = b + c and c>0, then a>b`

Answer 10

Ohhh, thank you!

Answer 11

look back at the previous step where it says `∠1 = ∠3 + ∠2`

Answer 12

you're welcome