4. given abc with vertices at a(1,-4), b(-1,-2), and c(-2,-5), prove or disprove that abc is isosceles

ABC is isosceles

Step-by-step explanation:

The coordinate of points given are:

A(1,-4)

B(-1, -2 )

C ( -2 , -5 )

For ABC to be isosceles , then AB must be equal to BC or AB = AC

The next thing to do  is to find the value of AB , BC and AC using the formula for finding distance between two points which is given by:

D =

Calculating AB first , we have

=

=

Therefore:

AB =

Calculating BC , we have :

D =

D =

D =

Therefore:

BC =

Calculating AC , we have :

D =

D =

D =

Therefore:

AC =

Since AC = BC then triangle ABC is isosceles

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.