Question

Given that S is the midpoint of RT. US = RS Prove that SUT is an isosceles triangle.

Answer 1

Hint: Now note that to prove the triangle is isosceles we will prove that two sides of the triangle are equal. Now we are given that S is the midpoint of RT hence we have RS = ST. Now we are given that SU = RS. Hence using transitivity we will prove two sides of the triangle are equal.

Complete step-by-step solution:
Now a closed figure with n sides is called a polygon and a polygon with three sides is called triangle. Now based on the sides of the triangle we can classify the triangle in three types.
First is the equilateral triangle where all three parts of the triangle are equal. Next is isosceles triangle where any two sides of triangle are equal and third is scalene triangle where all the sides of triangle are of different length.
Now we know that in the line segment RT S is the midpoint. Hence distance of S from R is equal to distance of T from S. Hence we have RS = ST.
Now we are given that US = RS.
Now hence we have US = RS and RS = ST. Hence by property of transitivity we have US = ST.
Hence in the triangle SUT we have US = ST.
Hence two sides of the triangle are equal and the triangle is an isosceles triangle.

Note: Now note that the triangles can also be classified on the base of the angle in triangle. If any angle in the triangle is ${{90}^{\circ }}$ then the triangle is called a right angled triangle. If any angle in triangle is more that ${{90}^{\circ }}$ then the triangle is obtuse angled triangle and if all the angles in triangle are less than ${{90}^{\circ }}$ then the triangle is acute angled triangle.