2 Adjacent Sides, 3 Angles

Q. The construction of $\Delta ABC$, given that BC = 6cm, $\angle B={45}^{\circ }$ is not possible when the difference between AC and AB is equal to

1. 5.2 cm
2. 4.0 cm
3. 6.9cm
4. 5.0 cm

Q.

Construct Quadrilateral LIFT LI = 4 cm IF = 3 cm TL = 2.5 cm LF = 4.5 cm IT = 4 cm.
[3 MARKS]

Q. Can you construct a parallelogram, if the measure of two adjacent sides and two adjacent angles are given?

1. Yes
2. No
3. Data insufficient
4. Parallelogram can never be constructed

Q.

A kite can be constructed with

1. 2 adjacent angle and 2 non equal sides

2. 1 diagonal and a pair of equal sides

3. A pair of equal sides and equal angles

4. 2 diagonals

Q. DEFG is a quadrilateral with DE = 4.5 cm, EF = 6.5 cm, $\angle$D = 65°, $\angle$E = 100° and $\angle$F = 60°.
Arrange the steps of construction in the correct order.

(a) With E as centre and radius 6.5 cm, draw an arc. Mark the point to be F.

(b) Quadrilateral DEFG is constructed.

(c) Make ∠D = 65° and $\angle$E = 100° and extend the lines.

(d) Draw DE = 4.5 cm.

(e) Make $\angle$ F = 60° and extend the line. Mark the intersecting point of the lines to be G.

1. d, c, a, e, b
2. c, a, d, b, e
3. d, a, b, e, c
4. c, a, b, e, d

Q. Which of the following unique quadrilaterals can be constructed if the measure of only two adjacent sides are given?

1. Parallelogram
2. All of the above
3. Rectangle
4. Rhombus

Q.

A parallelogram can be constructed if:

1. One pair of opposite sides and an angle are given

2. Two adjacent sides and one angle are given

3. One side and one angle are given

4. One side and two angles are given

Q. Gokul is constructing a triangle XYZ where the $\angle X=30°$ and $\angle Y=100°$. Which of the following measurements is required to complete the construction?

1. XY = 6 cm
2. YZ = 6 cm
3. XZ = 6 cm
4. $\angle Z$ = 50°

Q. Construct a quadrilateral ABCD where AB = 8 cm, BC = 6 cm, DC = 4 cm. DC is parallel to AB and $\angle DCB$ is twice the angle ABC.

1. 
2. 
3. 
4. 

Q. Rearrange the steps of construction of the quadrilateral MORE where MO = 6cm, OR = 4.5cm, $\angle M=60°,\angle O=\angle R=105°$.


Steps of Construction:

(a) Draw a line segment MO of length 6 cm.
(b) Quadrilateral MORE is hence constructed.
(c) Mark the point to be R and construct another 105° at the point R.
(d) Extend the line and mark the intersecting point to be E.
(e) Construct 60° at the point M and 105° at the point O and extend the lines.
(f) With O as centre and 4.5 cm as the radius, construct an arc of length 4.5 cm

1. (a), (e), (f), (c), (b), (d)
2. (a), (b), (c), (d), (e), (f)
3. (a), (e), (f), (c), (d), (b)
4. (a), (e), (b), (d), (f), (c)

Q.

Can sum of opposite angles of a quadrilateral be 350?

Q.

What is drawn in the first step in constructing a quadrilateral for which 2 sides and 3 angles are known?

1. Line Segment

2. None of these

3. Arc

4. Triangle

Q. Ajay is constructing a quadrilateral ABCD where AB = 5 cm, BC = 3 cm, $\angle$DAB = 120°, $\angle$ABC = 110° and $\angle$DCB = 90°.
He is constructing as follows:

Step 1:
Step 2:
What will be step 3?

1. 
2. 
3. None of the above.
4. 

Q. For drawing a quadrilateral when 2 sides and 3 angles are given, the length of any 2 sides is sufficient. State whether true or false.

1. False
2. True

Q. It is not possible to construct $\Delta \text{ABC}$ given that BC = 5.5 cm and $\angle C={60}^{\circ }$, when sum of the measures of AB and AC equal to ___.

1. 5.9 cm
2. 6 cm
3. 4.5 cm
4. 5.7 cm

Q. Can we draw a quadrilateral uniquely with the following data? Suppose that, PQRS is the quadrilateral with PQ = 4 cm, $\angle P$ = ${80}^{\circ }$, $\angle Q$ = ${105}^{\circ }$, $\angle R$ = ${80}^{\circ }$.

1. We can construct a quadrilateral but not uniquely
2. We can uniquely construct a quadrilateral
3. Yes
4. No

Q. The construction of a $\Delta ABC,$ given that BC = 3cm, $\angle C={60}^{\circ }$ is possible, when the difference between AC and AB is equal to

1. 3.2 cm
2. 3 cm
3. 2.8 cm
4. 3.1 cm

Q. The minimum number of angles required in addition to the measure of two sides, to construct a parallelogram equal to

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

Q.

Given the three angles of a quadrilateral, for construction we also need to know the length of

1. two adjacent sides

2. one side

3. any two sides

4. two opposite sides

Q. Construct the quadrilaterals with the given measurement and write step of construction.
i) Quadrilateral ABCD with AB = 5.5 cm , BC=3.5 cm , CD = 4 cm , AD = 5 cm and $\angle A={45}^{\circ }$

Q.

Construct a quadrilateral JUMP in which JU = 3.5 cm, UM = 4 cm, MP = 5 cm, PJ = 4.5 cm, and diagonal, PU = 6.5 cm.

Q. The number of triangles that we can see after the construction of a quadrilateral when 2 adjacent sides and 3 angles are given will be .

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

Q. Construct a quadrilateral EFGH, where EF = 6cm, FG = 5.2 cm, $\angle E=75°$, $\angle F=\frac{2}{3}\angle G$ and $\angle F+\angle G=150°$. Measure the value of $\angle H$.

1. 135°
2. 115°
3. 125°
4. 85°

Q. Question 130
State whether the statements are True or False.
A parallelogram can be constructed uniquely, if both diagonals and the angle between them is given.

Q.

Given the three angles of a quadrilateral, for construction we also need to know the length of

1. two adjacent sides

2. two opposite sides

3. one side

4. any two sides

Q. For constructing a unique quadrilateral when 2 sides and 3 angles are given, the length of sides are mandatory.

1. two opposite
2. two adjacent
3. any two

Q.

If the measure of sides of quadrilaterals are given as AB = 4cm, CD = 5 cm, and angles are given as ∠ABC=${75}^{\circ }$, ∠BCD=${45}^{\circ }$ and ∠CDA=${135}^{\circ }$. Can you construct a unique quadrilateral ABCD?

1. With measure of $\angle$DAB, Yes

2. Yes

3. No

4. With measure of BC, Yes

Q. The number of triangles that we can see after the construction of a quadrilateral when 2 adjacent sides and 3 angles are given will be .

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

Q. The number of triangles that we can see after the construction of a quadrilateral when 2 adjacent sides and 3 angles are given will be .

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

Q. The number of triangles that we can see after the construction of a quadrilateral when 2 adjacent sides and 3 angles are given will be .

1. \N
2. 1
3. 2
4. 3