Construction of Triangles When Two Sides and the Included Angle Are Given

Q. How we can draw a unique triangle

Q.

In the given figure AB||CD If $\angle ABE=60$ and $\angle EFD={35}^{\circ },$ then x = ___

1. ${20}^{\circ }$

2. ${25}^{\circ }$

3. ${30}^{\circ }$

4. ${60}^{\circ }$

Q.

Question 4 (b)

Try to construct triangles using matchsticks. Some are shown here. Can you make a triangle with:

4 matchsticks?

(Remember you have to use all the available matchsticks)
Name the type of triangle. If you cannot make a triangle, think of reasons for it.

Q.

For constructing a triangle, we must know two sides and an 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. Given that AB = 4cm and BC = 6.5cm , which of the following information is required to construct $△ABC$?

1. None of the above
2. $\angle ACB$ = ${60}^{\circ }$
3. $\angle ABC$ = ${60}^{\circ }$
4. AD = 3 cm

Q. The minimum number of triangles that can be drawn if two sides and one angle have been given is:

1. 3
2. 2
3. 1
4. 0

Q. Which of the following step is not required to construct a $△ABC$, when AB= 3cm, BC= 5cm and $\angle ABC={60}^{\circ }$.

1. Draw a rough sketch of the triangle. Draw BC = 5cm.
2. With the help of compass, construct $\angle PBC={60}^{\circ }$.
3. With B as centre, draw an arc of 3cm length which cuts BP at point A.
   $\therefore$ BA = 3cm.
   Join A and C.
4. With the help of compass, construct $\angle PAC={60}^{\circ }$.

Q.

If the angles of a triangle are in the ratio 1 : 2 : 3, then based on the angles, the triangle is ___.

1. Side, Side, Angle

2. Side, Angle, Side

3. Angle, Angle, Angle

4. Angle, Angle, Side

Q. Construct $\Delta$DEF such that DE $=5$ cm, DF $=3$ cm and $\angle$EDF = ${90}^{\circ }$.
[3 marks]

Q.

For constructing $\Delta$LMN exactly identical to $\Delta$ABC, choose from the options, the measurements required.

1. LM, MN and LN

2. LM, MN, LN and ∠MLN

3. LM, MN, LN, ∠MLN and ∠MNL

4. MN and LN