R Chandra Solutions for Chapter: Triangles, Exercise 5: TEST YOUR SKILLS

$\mathrm{A}\mathrm{D}$ is a median of $∆\mathrm{A}\mathrm{B}\mathrm{C}$. Which of the following is not true?
$\left(\mathrm{i}\right)\mathrm{}\mathrm{A}\mathrm{B}+\mathrm{B}\mathrm{C}>\mathrm{A}\mathrm{D}$
$\left(\mathrm{i}\mathrm{i}\right)\mathrm{}\mathrm{A}\mathrm{C}+\mathrm{B}\mathrm{C}>\mathrm{A}\mathrm{D}$
$\left(\mathrm{i}\mathrm{i}\mathrm{i}\right)\mathrm{}\mathrm{A}\mathrm{B}+\mathrm{B}\mathrm{C}<\mathrm{A}\mathrm{D}$

Which of the following form a set of sides of a triangle?
$\left(\mathrm{i}\right)\mathrm{}10\mathrm{c}\mathrm{m},\mathrm{}5\mathrm{c}\mathrm{m},\mathrm{}4\mathrm{c}\mathrm{m}$
$\left(\mathrm{i}\mathrm{i}\right)\mathrm{}8\mathrm{c}\mathrm{m},\mathrm{}6\mathrm{c}\mathrm{m},\mathrm{}3\mathrm{c}\mathrm{m}$
$\left(\mathrm{i}\mathrm{i}\mathrm{i}\right)\mathrm{}5\mathrm{c}\mathrm{m},\mathrm{}2.5\mathrm{c}\mathrm{m},\mathrm{}1.9\mathrm{c}\mathrm{m}$

Which of the following form a set of angles of a triangle?
(i) $35°\mathrm{}45°,95°\mathrm{}$
(ii) $40°,\mathrm{}50°,100°\mathrm{}$
(iii) $21°,\mathrm{}39°,120°$

In the figure $\mathrm{\angle }\mathrm{B}<\mathrm{\angle }\mathrm{A}$ and $\mathrm{\angle }\mathrm{C}<\mathrm{\angle }\mathrm{D}$ then which of the following is true?

$\left(\mathrm{i}\right)\mathrm{}\mathrm{A}\mathrm{D}=\mathrm{B}\mathrm{C}$
$\left(\mathrm{i}\mathrm{i}\right)\mathrm{}\mathrm{A}\mathrm{D}<\mathrm{B}\mathrm{C}$
$\left(\mathrm{i}\mathrm{i}\mathrm{i}\right)\mathrm{}\mathrm{A}\mathrm{D}>\mathrm{B}\mathrm{C}$

In the figure, $\mathrm{\angle }\mathrm{B}=55°$. If $\mathrm{D}$ is the midpoint of $\mathrm{B}\mathrm{C}$ and $\mathrm{A}\mathrm{B}=\mathrm{A}\mathrm{C}$, what is the measure of $\mathrm{\angle }\mathrm{B}\mathrm{A}\mathrm{D}$?

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $2:3$, then what is the measure of the greater of the two angles?

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. What is the measure of these equal angles?

In the given figure $\mathrm{Q}\mathrm{P}\left|\right|\mathrm{R}\mathrm{S}$, $\mathrm{\angle }\mathrm{O}\mathrm{P}\mathrm{Q}=110°$ and $\mathrm{\angle }\mathrm{Q}\mathrm{R}\mathrm{S}=130°$ , then find the value of $\mathrm{\angle }\mathrm{P}\mathrm{Q}\mathrm{R}$.