Construction of Triangles: When 2 Sides and Included Angle Are Given

Q. In $△$ XYZ , $\overline{XY}$ =6.3 cm and $\overline{XZ}$ = 7 cm. Which is the correct information needed to construct the triangle?

1. $\angle$ Z = 45°
2. None of the above
3. $\angle$ X = 85°
4. $\angle$ Y = 50°

Q.

Construct a right angle triangle ABC in which hypotenuse $\mathrm{AC}=5\mathrm{cm}$ and leg $\mathrm{AB}=3.5\mathrm{cm}$. Name the vertex at which angle is $90°$

Q.

Construct a right-angled triangle in which base is $6.3cm$ and the hypotenuse makes an angle of $30°$ with the base.

Q.

A triangle $PQR$can be constructed, when $m\angle Q={90}^o,$$QR=7cm$and $PR=9cm$using the _________ criterion.

1. $SAS$

2. $RHS$

Q. In $△$ ABC , $\overline{AB}$ =8.5 cm and $\overline{BC}$ = 9 cm. Which of the following is/are the correct information needed to construct the triangle?

1. $\angle$ A = 95°
2. $\angle$ B = 36°
3. $\angle$ C = 49°
4. $\overline{AC}$ =5 cm

Q. In $△$ XYZ , $\angle$ X = 50° and $\overline{XY}$ = 9.5 cm. Which is the correct information needed to construct the triangle?

1. $\overline{YZ}$ = 4.5 cm
2. $\angle$ Z = 100°
3. $\overline{XZ}$ = 4 cm
4. None of the above

Q.

A triangle $LMN$can be constructed when $\angle LMN={90}^o,$$NL=5cm,$and $MN=3cm$by using the __________ criterion.

1. $SAS$

2. $RHS$

Q. In $△$ ABC , $\angle$ B = 90° and $\overline{AC}$ = 13 cm. Which of the following information is needed to construct the triangle?

1. $\angle$ A = 25°
2. $\overline{BC}$ = 5 cm
3. $\angle$ C = 65°
4. None of the above

Q.

A triangle $PQR$can be constructed when $\angle PQR={90}^o,$$RP=6.5cm$and $QR=4cm$

1. $SAS$

2. $RHS$

Q. With which of the following information , we can create $△$ ABC?

1. $\overline{AB}$ = 6 cm , $\overline{BC}$ = 8 cm, $\overline{AC}$ = 10 cm
2. $\angle$ B= 60° , $\angle$ C= 30° , $\overline{AC}$ = 10 cm
3. $\angle$ A= 90°, $\angle$ B= 60° , $\angle$ C= 30°
   
4. $\overline{AB}$ = 6 cm, $\overline{BC}$ = 8, $\angle$ C= 30°

Q. Steps for the construction of a right triangle LMN in which $\angle M={90}^{\circ }$, MN = 4 cm and LN = 6.2 cm is given below. Choose the correct order.

1. Draw a line segment XY.
2. Construct a line segment MP, sufficiently large such that $\angle NMP={90}^{\circ }$
3. With N as centre and radius 6.2 cm draw an arc, cutting MP at L, join NL.
4. Locate M and N on XY such that MN = 4 cm.

1. 1, 4, 2, 3
2. 1, 4, 3, 2
3. 2, 1, 3, 4
4. 2, 3, 1, 4

Q.

For constructing a triangle, we must know two sides and included angle. Which triangle can be uniquely constructed by knowing two sides and any other angle?

1. Right angled triangle

2. Scalene triangle

3. Isosceles triangle

4. Equilateral triangle

Q. We can draw a triangle ABC in which BC is 12cm, $\angle B$ is ${75}^{\circ }$ and AB + AC = 6.5 cm.

1. True
2. False
3. Data insufficient
4. Cannot be determined

Q. Steps for the construction of a triangle PQR of PQ=4cm, QR =5.2cm and $\angle Q={60}^{\circ }$ below. Choose the correct order.
1.Draw a line segment which is sufficiently long using ruler
2.At Q, construct a line segment QM, sufficiently large such that $\angle MQR={60}^{\circ }$
3.Locate points Q and R on it such that QR=5.2 cm
4.With Q as centre and radius as 4cm, draw an arc cutting QM at P, join PR.

1. 1, 2, 3, 4
2. 2, 1, 3, 4
3. 1, 3, 2, 4
4. 2, 3, 1, 4

Q. In $△$ CDE , $\angle$ C = 30° and $\overline{CD}$ = 8 cm. Which is the correct information needed to construct the triangle?

1. $△$ CDE is an isosceles triangle with base $\overline{DE}$
2. $△$ CDE is right angled at $\angle$E
3. $\overline{DE}$ = 11 cm and $\angle$ E = 80°
4. None of the above

Q. In $△$ ABC , $\angle$ B = 90° and $\overline{AC}$ = 13 cm. Which of the following information is needed to construct the triangle?