Question

Select all are true triangle ABC a scalene triangle ABC is isosceles triangle AB is equilateral

Answer 1

With the coordinates of the vertices of triangle ABC at A(-1, 3), B(-5, -1), C(3, -1), we have;

• Triangle ABC is an isosceles triangle

How can the type of a given triangle be found?

Taking the vertices of ∆ABC as found in a similar question online as A(-1, 3), B(-5, -1), C(3, -1), calculating the lengths of the sides of the triangle gives;

AB = √((-1 - (-5))² + (3 - (-1))²) = 4•√2

AC = √((-1 - 3)² + (3 - (-1))²) = 4•√2

BC = √((-5 - 3)² + (-1 - (-1))²) = 8

AB = AC = 4•√2

• Triangle ABC is an isosceles triangle by the definition of isosceles triangles.

(AB)² + (AC)² = (4•√2)² + (4•√2)² = 64 = (BC)²

Therefore;

(BC)² = (AB)² + (AC)²

Which indicates that triangle ABC is an isosceles right triangle.

Learn more about the types of triangles here:

brainly.com/question/1058720

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