Decide whether enough information is given to prove that the triangles are congruent using the ASA Congruence Theorem. If so, write a proof. If not, explain why. △WXZ, △YZX
A: yes; It is given that WZ||YX. ∠WXZ is supplementary to ∠ZWX and ∠WZX is supplementary to ∠XYZ by the Consecutive Interior Angles Theorem. Also, ZX≅ZX by the Reflexive Property of Congruence. So, △WXZ≅△YZX by the ASA Congruence Theorem.

B: yes; It is given that WZ||YX. ∠WXZ≅∠YZX and ∠WZX≅∠YXZ by the Alternate Interior Angles Theorem. Also, ZX≅XZ by the Reflexive Property of Congruence. So, △WXZ≅△YZX by the ASA Congruence Theorem.

C: no; there is only enough information to conclude that one pair of angles and one pair of sides are congruent. So, ASA does not apply in this case.

D: no; The information given applies to two angles and a non-included side. So, ASA does not apply in this case.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form