Question

What is true about △abc? select three options ab ⊥ ac the triangle is a right triangle. The triangle is an isosceles triangle. The triangle is an equilateral triangle. Bc ∥ ac.

Answer 1

The following are true:

• AB ⊥ AC
• The triangle is a right triangle.
• The triangle is an isosceles triangle.

What a triangle is?

A triangle is a shape with 3 sides and angles

TO get the correct options, we will find the measure of the sides AB, BC, and AC using the distance formula:

For the side AB:

$AB = \sqrt{(-5+1)^2+(-1-3)^2}\\AB = \sqrt{16+16}\\AB = \sqrt{32}\\AB = 4\sqrt{2}$

For the side AC:

$AC = \sqrt{(3+1)^2+(-1-3)^2}\\AC = \sqrt{16+16}\\AC = \sqrt{32}\\AC = 4\sqrt{2}$

For the side BC:

$BC = \sqrt{(-5-3)^2+(-1+1)^2}\\BC = \sqrt{64+0}\\BC = \sqrt{64}\\BC = 8$

Since two sides are equal AB = AC, hence the triangle is an isosceles triangle

From the figure, we can see that the angle between AB and AC is 90degrees, hence AB ⊥ AC and the triangle is a right triangle

Learn more on right triangles here: brainly.com/question/15739772