Match the reasons with the statements in the proof to prove DF = EF given that DEF is a triangle by definition and angles 3 and 4 are equal. Given:

△DEF

∠3 = ∠4

Prove:

DF = EF

1. ∠1 = ∠2
Two Angles Supplementary to Equal Angles are Equal to Each Other
2. DF = EF
Exterior Sides are in Opposite Rays
3. ∠3 = ∠4
Given
4. ∠1 and ∠3 are supplementary

∠2 and ∠4 are supplementary
If the Two Angles of a Triangle are Equal, then the Sides Opposite those Angles are also Equal

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign

y=3x+4

step-by-step explanation:

given the points a(0,4) and b(-4, -8)

eqn of line ab: (y-4)/(x-0)=(-8-4)/(-4-0)

(y-4)/x=-12/-4=3

y=3x+4

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)

-3.5 degrees per hour

step-by-step explanation:

find the unit rate:

-12   1/4 degrees           12.25 degrees

= - = -3.5 degrees per hour

      3   1/2 hours               3.5 hours