Mathematics, 28.08.2019 13:30, 2018jonw

Which statement proves that △xyz is an isosceles right triangle?
xz ⊥ xy
xz = xy = 5
the slope of xz is , the slope of xy is , and xz = xy = 5.
the slope of xz is , the slope of xy is , and the slope of zy = 7.

Which statement proves that △xyz is an isosceles right triangle? xz ⊥ xy xz = xy = 5 <

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answered: valeriegarcia12

In order for the triangle to be called an isosceles right triangle, it must satisfy both conditions: XZ and XY must be perpendicular to each other, and XZ = XY.
To determine whether two lines are perpendicular, their slopes must be negative reciprocals of each other.

Solving for the slopes of XZ and XY:
slope of XZ = (y₂-y₁) / (x₂-x₁) = (6-3)/(5-1) = 3/4
slope of XY = (y₂-y₁) / (x₂-x₁) = (3--1)/(1-4) = -4/3
-4/3 is the negative reciprocal of 3/4, therefore XZ and XY are perpendicular to each other.

Solving for distance:
XZ = √[(y₂-y₁)²+(x₂-x₁)²] = √[(6-3)²+(5-1)²] = 5
XY = √[(y₂-y₁)²+(x₂-x₁)²] = √[(3--1)²+(1-4)²] = 5

The slope of XZ is 3/4, the slope of XY is -4/3, and XZ = XY = 5.

answered: jaileen84

The product of the slope of XZ and XY is -1, and XZ = XY = 5. Hence. triangle XYZ is the right isosceles triangle.

If a triangle is right isosceles triangle, then it must have one angle of 90 degrees and two equal sides that is corresponding to that right angle.

If two lines are perpendicular to each other, then the product of the slope of the perpendicular lines must be equal to - 1.

The formula for finding the slope of the line from two known points is given as;

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Where m is the slope of the line.

Solving for the slopes of XZ and XY:

Slope of XZ = (y₂-y₁) / (x₂-x₁) = (6-3)/(5-1) = 3/4

Slope of XY = (y₂-y₁) / (x₂-x₁) = (3--1)/(1-4) = -4/3

Thus, the product of the slopes of XY and XZ is -1. Hence, both sides made an angle of 90 degrees.

Solving for distance:

XZ = √[(y₂-y₁)²+(x₂-x₁)²] = √[(6-3)²+(5-1)²] = 5

XY = √[(y₂-y₁)²+(x₂-x₁)²] = √[(3--1)²+(1-4)²] = 5

The product of the slope of XZ and XY is -1, and XZ = XY = 5. Hence. triangle XYZ is the right isosceles triangle.

To know more about the right isosceles triangle, please refer to the link:

link

answered: Guest

yes

step-by-step explanation:

answered: Guest

Any pictures or something i need more info

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Which statement proves that △xyz is an isosceles right triangle?
xz ⊥ xy
xz = xy = 5 <...