NCERT Solutions for Class 7 Maths Chapter 10 Practical Geometry (EX 10.3) Exercise 10.3

Q.1

$\mathrm{Construct}\mathrm{\Delta DEF}\mathrm{such}\mathrm{that}\mathrm{DE}=5\mathrm{cm},\mathrm{DF}=3\mathrm{cm}\mathrm{and}\mathrm{m}\angle \mathrm{EDF}=90\mathrm{°}.$

Ans.

\begin{array}{l}\text{The steps of construction are as follows:}\\ \text{(i) Draw a line segment DE of length 5 cm}\text{.}\end{array}

\text{(ii) At point D, draw a ray DX making an angle of 90}°\text{with DE}\text{.}

\begin{array}{l}\text{(iii) Taking D as centre, draw an arc of 3 cm radius}\text{. It will}\\ \text{intersect DX at point F}\end{array}

\text{(iv) Join F to E}

\text{Thus, DEF is the required triangle}\text{.}

Q.2

$\begin{array}{l}\mathrm{Construct}\mathrm{an}\mathrm{isosceles}\mathrm{triangle}\mathrm{in}\mathrm{which}\mathrm{the}\mathrm{lengths}\mathrm{of}\\ \mathrm{each}\mathrm{of}\mathrm{its}\mathrm{equal}\mathrm{sides}\mathrm{is}6.5\mathrm{cm}\mathrm{and}\mathrm{the}\mathrm{angle}\mathrm{between}\\ \mathrm{them}\mathrm{is}110\mathrm{°}.\end{array}$

Ans.

\begin{array}{l}\text{An isosceles triangle PQR has to be constructed with}\\ \text{PQ}=\text{QR}=\text{6}\text{.5 cm}\text{.}\\ \text{The steps of construction are as follows:}\\ \text{(i) Draw a line segment QR of length 6}\text{.5 cm}\end{array}

\text{(ii) At point Q, draw a ray QX making an angle 110}°\text{with QR}\text{.} \begin{array}{l}\end{array}

\begin{array}{l}\text{(iii) Taking Q as centre, draw an arc of 6}\text{.5 cm radius}\text{. It}\\ \text{intersects QX at point P}\text{.}\end{array}

\text{(iv) Join P to R to obtain the required triangle PQR}\text{.}

Q.3

$\mathrm{Construct}\mathrm{\Delta ABC}\mathrm{with}\mathrm{BC}=7.5\mathrm{cm},\mathrm{AC}=5\mathrm{cm}\mathrm{and}\mathrm{m}\angle \mathrm{C}=60\mathrm{°}.$

Ans.

\begin{array}{l}\text{The steps of constructions are as follows:}\\ \text{(i) Draw a line segment BC of length 7}\text{.5 cm}\text{.}\end{array}

\text{(ii) At point C, draw a ray CX making 60 with BC}\text{.} \begin{array}{l}\end{array}

\begin{array}{l}\text{(iii) Taking C as centre, draw an arc of 5 cm radius}\text{.}\\ \text{It intersect CX at point A}\text{.}\end{array}

\text{(iv) Join A to B to obtain the required triangle ABC}\text{.}