Question
Construct a triangle using the given data: $DE = 5\ cm, \angle D = 75^\circ $ and $\angle E = 60^\circ $
✓
Answer
$DE = 5\ cm, \angle D = 75^\circ $ and $\angle E = 60^\circ $
Steps of Construction:
$1.$ Draw a line segment $DE = 5\ cm.$
$2.$ With $D $as centre, draw an arc cutting $DE$ at $P.$
$3.$ With $P$ as centre and same radius, cut the arc at $Q$ and then from $Q,$ with same radius, cut the arc at $R.$
$4$. With $Q$ and $R$ as centre bisect $\angle RDQ$ thus formed to draw a ray $XD.$
$5.$ Again bisect the $\angle XDQ$. Let $DY$ be the bisector. $DY$ makes an angle of $75^\circ $ with $DE.$
$6.$ With $E$ as centre, draw an arc meeting $DE$ at $S.$
$8.$ Produce $ET$ to $EZ. EZ$ makes an angle of $60^\circ $ with $DE.$
$9.$ Mark the point as $F$, where $DY$ and $EZ$ cut each other.
Thus, $\text{DEF}$ is the required triangle.
Steps of Construction:
$1.$ Draw a line segment $DE = 5\ cm.$
$2.$ With $D $as centre, draw an arc cutting $DE$ at $P.$
$3.$ With $P$ as centre and same radius, cut the arc at $Q$ and then from $Q,$ with same radius, cut the arc at $R.$
$4$. With $Q$ and $R$ as centre bisect $\angle RDQ$ thus formed to draw a ray $XD.$
$5.$ Again bisect the $\angle XDQ$. Let $DY$ be the bisector. $DY$ makes an angle of $75^\circ $ with $DE.$
$6.$ With $E$ as centre, draw an arc meeting $DE$ at $S.$
$8.$ Produce $ET$ to $EZ. EZ$ makes an angle of $60^\circ $ with $DE.$
$9.$ Mark the point as $F$, where $DY$ and $EZ$ cut each other.
Thus, $\text{DEF}$ is the required triangle.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
$375$ persons can be accommodated in a room whose dimensions are in the ratio of $6 : 4 : 1.$ Calculate the area of the four walls of the room if the each person consumes $64\ m^3$ of air.
→The annual incomes of $A$ and $B$ are in the ratio $3 :4$ and their annual expenditure are in the ratio $5 : 7.$ If each $Rs. 5000;$ find their annual incomes.
→In parallelogram $\text{ABCD}$, the bisector of $\angle A$ meets $DC$ at $P$ and $AB = 2 AD$.Prove that:$(i) BP$ bisects angle $B.(ii)$ \Angle APB = 90^o$.
→In the given figure, side $B A$ of $\triangle A B C$ has been produced to D such that $CD = CA$ and side CB has been produced to E . If $\angle BAC =106^{\circ}$ and $\angle ABE =128^{\circ}$, find $\angle BCD$.
→Draw a histogram for the following frequency table:
→| Class interval | $5 - 9$ | $10 - 14$ | $15 - 19$ | $20 - 24$ | $25 - 29$ | $30 - 34$ |
| Frequency | $5$ | $9$ | $12$ | $10$ | $16$ | $12$ |
The figure shows the cross section of $0.2\ m$ a concrete wall to be constructed. It is $0.2\ m$ wide at the top, $2.0\ m$ wide at the bottom and its height is $4.0\ m$, and its length is $40\ m$. Calculate the cross sectional area
→In the given figure, $D$ and $E$ are points on $AB$ and $AC$ respectively. $AE$ and $CD$ intersect at $P$ such that $AP = CP$. If $\angle BAE = \angle BCD$, prove that $\text{DBDE}$ is isosceles.
→Solve :$\frac{3}{2 x}+\frac{2}{3 y}=-\frac{1}{3}; \frac{3}{4 x}+\frac{1}{2 y}=-\frac{1}{8}$
→In a parallelogram $\text{PQRS, M}$ and $N$ are the midpoints of the opposite sides $PQ$ and $RS$ respectively. Prove that;$RN$ and $RM$ trisect $QS.$
→In the given figure, $AB = AC$. Show that $AD > AB$.
→