The correct option is 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 .
Right triangle:
A right angled triangle or right triangle is a triangle in which one angle of triangle is equal to .
Acute triangle:
An acute angled triangle is a triangle in which all the three angles are less than .
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 and .
The side AS is common to both the triangles and the and 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 and 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 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.