Question

Which statement proves that △XYZ is an isosceles right triangle?

Answer 1

The second statement does lol

Answer 2

Answer:

XZ = XY = 5 units  are equal .

ΔXYZ is a Right isosceles triangle .

Step-by-step explanation:

As to an triangle is isosceles triangles the two sides of the triangle must be equal .

Formula

$Distance\ formula = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

As the vertices of the ΔXYZ be X (1,3) , Y (4,-1) and Z(5,6) .

$XY = \sqrt{(4-1)^{2}+(-1-3)^{2}}$

$XY = \sqrt{(3)^{2}+(-4)^{2}}$

$XY = \sqrt{9+16}$

$XY = \sqrt{25}$

$\sqrt{25}= 5$

$XY = 5\ units$

$YZ = \sqrt{(5-4)^{2}+(6-(-1))^{2}}$

$YZ = \sqrt{(1)^{2}+(7)^{2}}$

$YZ = \sqrt{1+49}$

$YZ = \sqrt{50}\ units$

$ZX = \sqrt{(1-5)^{2}+(3-6)^{2}}$

$ZX = \sqrt{(-4)^{2}+(-3)^{2}}$

$ZX = \sqrt{16+9}$

$ZX = \sqrt{25}$

$\sqrt{25}= 5$

ZX = 5 units

Thus XZ = XY = 5 units  are equal .

Therefore ΔXYZ is a Right isosceles triangle .