Triangle xyz is shown on the coordinate grid. which statements are true about triangle xyz? xy measures √26units. yz measures √56 units. zx measures √34 units. xyz is an isosceles triangle. xyz is a right triangle. xyz is a scalene triangle.

XY measures √26units.

XYZ is an isosceles triangle.

XYZ is a right triangle.

Step-by-step explanation:

The given triangle has vertices

We now apply the distance formula to find the length of all sides to obtain;

The length of YZ is

The length of ZX is

Since

The triangle is isosceles.

Slope of XZ

Slope of XY

Since

The triangle is a right angle triangle.

Solution:

Distance between two points in two dimensional coordinate plane is given by:

As, Converse of Pythagorean theorem states that if sum of squares of any two adjacent sides in a triangle is equal to Square of length of third side, then the triangle is right angled triangle.

The true statement about the triangle XYZ is

1. XY measures √26units.

2. XYZ is an isosceles triangle.

3. XYZ is a right triangle.