Embibe Experts Solutions for Chapter: Triangles, Exercise 1: CBSE-2023 (Delhi - I)

Prove that the area of an equilateral triangle described on one side of the square is equal to half the area of the equilateral triangle described on one of its diagonal.

In an equilateral $△ABC$, $D$ is a point on side$BC$, such that$BD=\frac{1}{3}BC$. Prove that $9A{D}^2=7A{B}^2$.

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

Given $∆ABC~∆PQR$,  if $\frac{AB}{PQ}=\frac{1}{3}$, then $\frac{ar\left(∆ABC\right)}{ar\left(∆PQR\right)}=$_____

$\mathrm{ABC}$ is an equilateral triangle of side $2\mathrm{a}$, then length of one of its altitude is $a\sqrt{x}$. The value of $\mathrm{a}$ is _____.

In Fig 2, $DE\parallel AC$ and $DC\parallel AP$. Prove that $\frac{BE}{EC}=\frac{BC}{CP}$

In figure, $\angle D=\angle E$ and $\frac{AD}{DB}=\frac{AE}{EC}$, prove that $BAC$ is an isosceles triangle.

In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite to its first side is a right angle.