When Two Sides and Their Included Angle Are Given

Q.

Construct a triangle whose sides are $3.6\mathrm{cm}$, $3.0\mathrm{cm}$ and $4.8\mathrm{cm}$. Bisect the smallest angle and measure each part.

Q.

Statement 1: It is possible to construct a unique triangle when the measurements of two sides and non-included angle are given.

Statement 2: It is possible to construct a triangle when the measurements of two sides and included angle are given.

Choose the correct option.

1. Both the statements are false
2. Statement $1$ is right and Statement $2$ is wrong
3. Statement $2$ is right and Statement $1$ is wrong
4. Both the statements are correct

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.

Which of the following data is not sufficient to draw a unique triangle?

1. Side, Side, Angle(not included)

2. Side, Angle(included), Side

3. Angle, Angle, Angle

4. Angle, Angle, Side(not included)

Q. Postulate used in the construction of isosceles triangle when base and length of altitude is given is:

1. SAS
2. ASA
3. RHS
4. SSS

Q.

Construct a triangle ABC in which BC is 5 cm, Angle B is ${120}^{\circ }$ and AB+AC=17cm [3 MARKS]

Q.

Which of the following play an important role in the Triangle construction 1?

1. Isoceles triangle

2. Equilateral Triangle

3. Congruent triangle

4. Similar Triangle

Q.

Akash was given lengths of two sides and the measure of an angle which is not included between the two sides. But still he was able to draw the triangle. So what should be the angle that was given? (in degrees)

__

Q.

The minimum number of triangles that can be drawn if two sides and one angle has been given is __.

Q.

To draw a right angle triangle:

1. The measure one more angle is needed

2. The length of one side is needed

3. The length of hypotenuse is needed

4. The length of any two sides is needed

Q.

The minimum number of triangles that can be drawn if two sides and one angle has been given is __.

Q. Given AB = 3 cm, AC = 5 cm and $\angle B={30}^{\circ }$, $\Delta$ABC cannot be uniquely constructed, with AC as base, why?

1. Two sides and included angle are given.
2. The other two angles are not given.
3. The vertex B cannot be uniquely located.
4. The vertex A coincides with the vertex C.

Q. Postulate which not used to prove congruency is:

1. SSS
2. ASS
3. ASA
4. AAS

Q. Which of the following data is not sufficient to draw a unique triangle?

1. Side, Side, Side
2. Side, Side, Angle(not included)
3. Side, Angle(included), Side
4. Angle, Angle, Side(not included)

Q. The construction of a triangle is not possible when

1. its perimeter and two base angles are given
2. its base, a base angle and the sum of other two sides are given
3. its base, a base angle and the difference of other two sides are given
4. its base, a base angle and perimeter are given