The correct option is [tex]\boxed{\bf option D}[/tex] 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 [tex]90^{\circ}[/tex].
Right triangle:
A right angled triangle or right triangle is a triangle in which one angle of triangle is equal to [tex]90^{\circ}[/tex].
Acute triangle:
An acute angled triangle is a triangle in which all the three angles are less than [tex]90^{\circ}[/tex].
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 [tex]\triangle\text{UAS}[/tex] and [tex]\triangle\text{VAS}[/tex].
The side AS is common to both the triangles and the [tex]\angle\text{USA}[/tex] and [tex]\angle\text{VSA}[/tex] 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 [tex]\triangle\text{UAS}[/tex] and [tex]\triangle\text{VAS}[/tex] 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 [tex]\boxed{\bf option D}[/tex] i.e., isosceles triangle.
Learn more:
1. Problem on -intercept of the quadratic equation https://brainly.com/question/1332667
2. Problem on the center and radius of an equation https://brainly.com/question/9510228
3. Problem on the general form of the equation of the circle https://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.
