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IgorLugansk [536]
3 years ago
6

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

Mathematics
2 answers:
Lisa [10]3 years ago
8 0
The second statement does lol

Papessa [141]3 years ago
3 0

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 .




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