Chhattisgarh Board Solutions for Exercise 12: Exercise – 4

We are given a trapezium $ABCD$ in which $\mathrm{AB}\Vert \mathrm{DC}$ and its diagonals intersect at point $O$. If $\mathrm{AB}=2\mathrm{CD},$ then find the ratio of the area of triangle $AOB$ and $COD$.

If the areas of two similar triangles are equal to each other, then prove that the triangles are congruent.

Prove that the ratio of the area of two similar triangles is the square of the ratio of their corresponding medians.

Sahid is trying to estimate the height of a pole. He is standing in such a manner that the shadow of his head '$H$' and the shadow of the top of the pole '$Q$' fall on the same point, $D$. If $\mathrm{DE}=1.6 \mathrm{m}$, $HE=2 \mathrm{m}$ and $DF=4.4 \mathrm{m}$, then the height of the pole is $\mathrm{k} \mathrm{m}$. Find the value of $k$

In the figure, which two triangles are similar to the triangle $\mathrm{ABC}$? Name them.

Find the value of $x$ and $y$.

$ABC$ and $BDE$ are two equilateral triangles such that $D$ is the midpoint of side $BC$. Ratio of area of triangles $\mathrm{ABC}$ and $\mathrm{BDE}$ is

If in two similar triangles $9ar\left(\mathrm{ABC}\right)=16ar\left(\mathrm{PQR}\right)$, then the value of $\frac{AB}{PQ}$ is