Embibe Experts Solutions for Chapter: Similar Triangles, Exercise 1: Exercise

In the given figure, $ABC$ is a triangle right-angled at $B$. $D$ and $E$ are points on $BC$ trisect it. Prove that $8A{E}^2=3A{C}^2+5A{D}^2$.

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

$ABC$ is an isosceles triangle right-angled at $B$. Equilateral triangles $ACD$ and $ABE$ are constructed on sides $AC$ and $AB$. Find the ratio between the areas of $∆ABE$ and $∆ACD$.

$△ABC~△DEF$. $BC=3 \mathrm{cm}, EF=4 \mathrm{cm}$ and area of $△ABC=54 {\mathrm{cm}}^2$. Determine the area $△DEF$.

The area of two similar triangles are $81 {\mathrm{cm}}^2$ and $49 {\mathrm{cm}}^2$ respectively. The altitude of the bigger triangle is $4.5 \mathrm{cm}$. Find the corresponding attitude of the smaller triangle.

Are triangles formed in a figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form.

Are triangles formed in a figure similar? If so, name the criterion of similarity. Write the similarity relation in symbolic form.

If $△\mathrm{ABC}, \mathrm{DE}\parallel \mathrm{BC}, \mathrm{AD}=2 \mathrm{cm}, \mathrm{DE}=3 \mathrm{cm} \mathrm{and} \mathrm{AB}=6 \mathrm{cm}$, then $\mathrm{BC}=$_____$\mathrm{cm}$.