Construction of Triangles When Two Angles and Included Side Are Given

Q.

Construct a ${60}^{\circ }$ angle using a line segment of length of length 10 cm.
[2 MARKS]

Q. Which of the following step is not required to construct a $△ABC$, when AB= 4cm, $\angle A={60}^{\circ }$ and $\angle B={30}^{\circ }$.

1. At B, draw BQ making an angle of ${30}^{\circ }$ with AB, i.e, draw angle QBA = ${30}^{\circ }$.
2. Draw AB = 4cm. At A, draw AP making an angle of ${60}^{\circ }$ with AB, i.e, draw angle PAB = ${60}^{\circ }$.
3. Draw a perpendicular bisector from point A and cut an arc at length 4cm from the foot of the perpendicular bisector
4. AP and BQ intersect each other at point C.

Q. Construct $△$ XYZ such that XY $=8$ cm, $\angle$X $={40}^{\circ }$, and $\angle$Y $={95}^{\circ }$. Find the length of YZ.
[3 marks]

Q. Given that $\angle A={50}^{\circ }$ and $\angle B={60}^{\circ }$ , which of the following information is required to construct $△ABC$?

1. Length AB = 4cm
2. Length BC = 4cm
3. Length AC = 4cm
4. None of the above

Q.

Construct $∆\mathrm{ABC}$, given $\mathrm{m}\angle \mathrm{A}=60°,\mathrm{m}\angle \mathrm{B}=30°$and $\mathrm{AB}=5.8\mathrm{cm}$.

Q.

Draw a triangle $\mathrm{ABC}$ with side $\mathrm{BC}=7\mathrm{cm},\angle \mathrm{B}=45°,\angle \mathrm{A}=105°$. Then, construct a triangle whose sides are $\frac{4}{3}$ times the corresponding sides of $∆ABC$. Give the justification of the construction.

Q.

Dean and Sam had to construct a triangle ABC with $\angle A={60}^{\circ }$, $\angle B={105}^{\circ }$ and BC = 5 cm. Assuming Dean and Sam both won't commit any error while construction, which of the following options is true?

1. They both will end up with different triangles

2. They both will end up with the same triangle

3. They can't complete the construction because such a triangle doesn't exist

4. Insufficient data for construction

Q. Question 4
Write True or False and give reasons for your answer:

A $\Delta ABC$ can be constructed in which BC = 6cm, $\angle C={30}^{\circ }$ and AC – AB = 4cm.

Q.

Find the sum of the angles of the $△ABD$.

​​

1. ${180}^{\circ }$

2. ${360}^{\circ }$

3. ${300}^{\circ }$

4. ${90}^{\circ }$

Q.

It is possible to construct a $△$ ABC in which $\angle A={95}^{\circ }$, AB = 5 cm and $\angle C={105}^{\circ }$

1. True

2. False

Q. In the given figure, $ABC$ is an equilateral triangle and $P$ is any point in $AC$; then $BP>PA$?
State true or false.

1. True
2. False

Q.

A $∆PQR$can be constructed, when $PQ=5.3cm,$$m\angle PQR={105}^o$and $m\angle QRP={40}^o$using the ________ criterion.

1. $SAS$

2. $ASA$

Q. Can you construct triangle ABC with AB = 5 cm, ang A = 80 deg, ang B = 120 deg?

1. Yes
2. No
3. Maybe
4. Poor Data