Dr. Sanjeev Verma and R.K. Tyagi Solutions for Chapter: Properties of Triangles, Exercise 5: CHAPTER-END EXERCISES

In the following figure, the sides $BC, CA$ and $AB$ of $∆ABC$ are produced in the order forming exterior angles $\angle ACD, \angle BAE$ and $\angle CBF$. Show that $\angle ACD +\angle BAE+\angle CBF=360°$.

Can the following be the sides of a triangle?

$2 \mathrm{cm}, 3 \mathrm{cm}, 5 \mathrm{cm}$

Can the following be the sides of a triangle?

$4 \mathrm{cm}, 3 \mathrm{cm}, 5 \mathrm{cm}$

Can the following be the sides of a triangle?

$6 \mathrm{cm}, 8 \mathrm{cm}, 7 \mathrm{cm}$

Can the following be the sides of a triangle?

$45 \mathrm{mm}, 50 \mathrm{mm}, 135 \mathrm{mm}$

In the figure, $AD\perp BC, AB=15 \mathrm{cm}, CD=5 \mathrm{cm}$ and $AC=13 \mathrm{cm}$. Calculate the lengths of sides $AD$ and $BC$.

Sides $BC, CA$ and $BA$ of a triangle $ABC$ are produced to $D, Q, P$, respectively as shown in the figure. If $\angle ACD=100°$ and $\angle QAP=35°$, find all the angles of the triangle $ABC$.

In the following figure, $∆ABC$ is equilateral. Find the measure of all the exterior angles i.e. $\angle FAB, \angle DBC$ and $\angle ACE$. Are they all same?