Embibe Experts Solutions for Chapter: Triangles, Exercise 1: Jharkhand Board-2018

All squares are- Similar or Congruent

$ABCD$ is a trapezium in which $AB\parallel CD$ and its diagonal $AC$ and $BD$ intersect each other at the point $O$,show that,
$\frac{OA}{OC}=\frac{OB}{OD}$

Prove that if a line is drawn parallel to one side of triangle to intersect the other two points in distinct point the other two points are divided in the same ratio.

Are all triangles similar-Equilateral or Isosceles.

$ABC$ is an isosceles triangle with $AC=BC$.If $A{B}^2=2A{C}^2$,then prove that,$ABC$ is a right angle triangle.

Prove that in a right triangle,the square of hypotenuse is equal to the sum of squares of the other two sides.

$ABC$ is an isosceles triangle right angled at $C$. Prove that $A{B}^2=2A{C}^2$.

Prove that if a line is drawn parallel to one side of triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.