Question

For the given triangle, the slope of zx is , the slope of zy is , and the slope of xy is 2. which statement verifies that triangle xyz is a right triangle? the slopes of zx and zy are opposite reciprocals. the slopes of xy and zy are opposite reciprocals. the slopes of zx and zy have opposite signs. the slopes of xy and zy have opposite signs.

Answer 1

The statement verifying triangle XYZ is a right triangle is that the slopes of ZX and ZY are opposite reciprocals, which means they satisfy the condition that one's slope is the negative inverse of the other.

Step-by-step explanation:

To determine whether triangle XYZ is a right triangle, we can use the slopes of its sides. A property of right triangles is that the slopes of the perpendicular sides are opposite reciprocals of each other. This means that if one side has a slope of m, the perpendicular side will have a slope of -1/m

Given that the slope of XY is 2, for XYZ to be a right triangle, either ZX or ZY must have a slope of -1/2. If the slope of ZX and ZY are opposite reciprocals, this means that if one is m, the other must be -1/m. Therefore, the statement that verifies XYZ is a right triangle is that the slopes of ZX and ZY are opposite reciprocals.

Answer 2

A statement which verifies that triangle XYZ is a right triangle is: B. The slopes of XY and ZY are opposite reciprocals.

In Mathematics and Geometry, perpendicular lines refers to two (2) lines that intersect or meet each other at an angle of 90° (right angles).

In Mathematics and Euclidean Geometry, a condition that is true for two lines to be perpendicular is given by:

`m_1 * m_2 = -1`

Since the slopes of XY and ZY are opposite reciprocals, we wcan reasonably infer and logically deduce that triangle XYZ is a right triangle because it consist of perpendicular segments;

-1/2 × 2 = -1

Complete Question:

For the given triangle, the slope of ZX is 1/3, the slope of ZY is -1/2, and the slope of XY is 2.

Which statement verifies that triangle XYZ is a right triangle?

The slopes of ZX and ZY are opposite reciprocals.

The slopes of XY and ZY are opposite reciprocals.

The slopes of ZX and ZY have opposite signs.

The slopes of XY and ZY have opposite signs.