Question

Is a perpendicular bisector of .

Answer 1

UV is a perpendicular bisector of RT. A perpendicular bisector UV is a line that does two things:

• cuts the line segment RT into two equal pieces or bisects it;
• makes a right angle with the line segment RT (is perpendicular).

Consider an arbitrary point X on the line RT that differs from S. Connect  points U, V and X to form triangle UVX. Line XS will be the height and the median of the triangle UVX. This gives you that triangle UVX will be isosceles triangle with base UV.

Answer: correct choice is D

Answer 2

The correct option is $\boxed{\bf option D}$ i.e., isosceles triangle.

Further explanation:

Given:

UV is a perpendicular bisector of RT.

Definition used:

A perpendicular bisector is a line which bisects a line at an angle of $90^{\circ}$.

Right triangle:

A right angled triangle or right triangle is a triangle in which one angle of triangle is equal to $90^{\circ}$.

Acute triangle:

An acute angled triangle is a triangle in which all the three angles are less than $90^{\circ}$.

Equilateral triangle:

An equilateral triangle is a triangle in which all the three sides and the angles are equal.

Isosceles triangle:

An isosceles triangle is a triangle in which two sides equal and two angles are equal.

Calculation:

Since, UV is a perpendicular bisector of RT, therefore the length of US and SV are equal.

Let A be any point on RT as shown in Figure 1.

Now, we will join the point A with U and V as shown in Figure 2.

From Figure 2, it is observed that the point A is common for  two triangles $\triangle\text{UAS}$ and $\triangle\text{VAS}$.

The side AS is common to both the triangles and the $\angle\text{USA}$ and $\angle\text{VSA}$ are both right angled.

Since RT is a perpendicular bisector of UV, therefore, the length US and VS are equal.

From Side-Angle-Side congruency, the $\triangle\text{UAS}$ and $\triangle\text{VAS}$ are congruent.

In congruent triangles the corresponding parts are also equal.

Therefore, the side UA and the side VA are equal.

Now, the triangle formed by the points U, V and A forms an isosceles triangle, since two sides are equal.

This implies that the triangle formed by points U, V and any other point other than S is an isosceles triangle.

Therefore, the correct option is $\boxed{\bf option D}$ i.e., isosceles triangle.

Learn more:

1. Problem on  -intercept of the quadratic equation brainly.com/question/1332667

2. Problem on the center and radius of an equation brainly.com/question/9510228

3. Problem on the general form of the equation of the circle brainly.com/question/1506955

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Triangles

Keywords:  Perpendicular bisector, triangle, points U, V, S, right triangle, acute triangle, obtuse triangle, isosceles triangle, Side Angle Side, SSS.