Construct an isosceles triangle with a base of length $8 \mathrm{c}\mathrm{m}$ and the equal sides measuring $5 \mathrm{c}\mathrm{m}$ each.

The steps to construct a $∆\mathrm{PQR}$ in which $\mathrm{PQ}=4 \mathrm{cm}, \mathrm{QR}=6 \mathrm{cm}$ and $\mathrm{\angle }\mathrm{PQR}=60°$are given below in a jumbled order. Arrange the steps in the correct order.

(a) With $\mathrm{Q}$ as the centre and a radius of $4 \mathrm{cm}$, draw an arc on ray $\mathrm{QX}$. Label the point of intersection as $\mathrm{P}$.

(b) Draw a line segment $\mathrm{QR}$ of length $6 \mathrm{cm}$.

(c) With the help of compasses, construct an angle $\angle \mathrm{XQR}$ of measure $60°$ at point $\mathrm{Q}$.

(d) Join points $\mathrm{P}$ and $\mathrm{R}$. $△\mathrm{PQR}$ is the required triangle.

The measurements $\mathrm{YZ}= 6 \mathrm{cm}, \angle \mathrm{X}=70°, \angle \mathrm{Z}=50°$ were given to construct triangle $\mathrm{XYZ}$ using $\mathrm{ASA}$ criterion. Construct the triangle and discuss whether the measurements are sufficient.

The steps to construct a $∆\mathrm{XYZ}$ where $\angle \mathrm{ZXY}=40°$, $\mathrm{\angle }\mathrm{XYZ}=95°$ and side $\mathrm{XY}=8 \mathrm{cm}$ are given below in a jumbled order. Arrange then in the correct order.

(a) Draw another ray $\mathrm{YQ}$ at point $\mathrm{Y}$ such that $\angle \mathrm{QYX}=95°$.

(b) Draw a line segment $\mathrm{XY}$ of length $8 \mathrm{cm}$.

(c) Name the point of intersection of the two rays, $\mathrm{PX}$ and $\mathrm{QY}$, as $\mathrm{Z}$. $△\mathrm{XYZ}$ is the required triangle.

(d) Draw a ray $\mathrm{XP}$ from point $\mathrm{X}$ such that $\angle \mathrm{PXY}=40°$.

Given below are the steps of constructing a $∆\mathrm{A}\mathrm{B}\mathrm{C}$ where $\mathrm{A}\mathrm{B}=8 \mathrm{c}\mathrm{m}, \mathrm{\angle }\mathrm{B}\mathrm{A}\mathrm{C}=30°$ and $\mathrm{\angle }\mathrm{A}\mathrm{B}\mathrm{C}=100°$. Complete them by filling in the blank.

(a) Draw a line segment $\mathrm{A}\mathrm{B}$ of length _____.

(b) Using a protractor draw a ray $\mathrm{A}\mathrm{P}$ from point $\mathrm{A}$ such that $\mathrm{\angle }$_____$=$_____$°$.

(c) Draw a ray $\mathrm{B}\mathrm{Q}$ from point $\mathrm{B}$ such that $\mathrm{\angle }$_____$=$_____$°$.

(d) Label the point of intersection of rays _____ and _____ as _____. $∆\mathrm{A}\mathrm{B}\mathrm{C}$ is the required triangle.