Mathematics - Practical Geometry
Exam Duration: 45 Mins Total Questions : 15
Given below are the steps of construction to construct a quadrilateral ABCD where AB = 5.6 cm, BC = 4.1 cm, CD = 4.4 cm, AD = 3.3 cm and ㄥA = 75°. Which of the following steps is INCORRECT?
Step 1 : Draw AB = 5.6 cm and construct ㄥBAX= 75°.
Step 2: With A as centre and radius = 3.3 cm, cut off AD = 3.3 cm along AX.
Step 3: Join BD. With D as centre and radius = 4.1 cm, draw an arc.
Step 4: With B as centre and radius = 4.1 cm, draw an arc to cut the arc drawn in above step at C. Join BC, CD to obtain the required quadrilateral ABCD.
- (a)
Step 1 only
- (b)
Step 2 only
- (c)
Step 3 only
- (d)
Step 4 only
It is possible to construct a quadrilateral with the sufficient data (other than five simple cases), where less than ______ parts but some other relations between them are given.
- (a)
Four
- (b)
Five
- (c)
Three
- (d)
Two
Arrange the steps of construction while constructing a parallelogram ABCD, given that AB = 5 cm, BC = 4 cm and ㄥB = 60°.
1. With A as centre and radius equal to 4 cm, draw an arc cutting AY at D.
2. At A, draw ㄥYAB = 120°.
[∴ A + B = 180°]
3. At B, draw ㄥXBA = 60°.
4. Draw AB = 5 cm.
5. Join CD.
6. With B as centre and radius equal to 4 cm, drawn an arc cutting BX at C.
- (a)
4, 3, 6, 2, 1, 5
- (b)
4, 3, 2, 6, 5, 1
- (c)
4, 6, 3, 1, 2, 5
- (d)
4, 3, 6, 2, 5, 1
Arrange the steps of construction while constructing a quadrilateral ABCD given AB = 5.1 cm, AD = 4 cm, BC = 2.5 cm, ㄥA = 60° and ㄥB = 850.
Step 1 : With B as centre and radius 2.5 cm, cut off BC = 2.5 cm along BY.
Step 2: Construct ㄥXAB = 60° at A.
Step 3: Join CD.
Step 4: With A as centre and radius 4 cm, cut off AD = 4 cm along AX.
Step 5: Draw AB = 5.1 cm.
Step 6: Construct ㄥABY = 85° at B.
- (a)
5, 2, 4, 1, 3, 6
- (b)
5, 4, 2, 1, 6, 3
- (c)
5, 2, 4, 6, 1, 3
- (d)
5, 2, 4, 1, 6, 3
If AB II DC, AB = 7 cm, BC = 6 cm, AD = 6.5 cm and ㄥB = 70°, then which figure can be constructed?
- (a)
Square
- (b)
Trapezium
- (c)
Rhombus
- (d)
Rectangle
Given below are the steps of construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, ㄥA = 75°, ㄥB = 105° and ㄥC = 120°. Which of the following steps is INCORRECT?
Step 1: Draw AB = 3.5 cm.
Step 2: Draw ㄥXAB = 75° at A and ㄥABY = 105° at B.
Step 3: With B as centre and radius BC = 6.5 cm, draw an arc to intersect BY at C.
Step 4: At C, draw ㄥADC = 120° such that CZ meets AX at D.
- (a)
Step 1 only
- (b)
Step 2 only
- (c)
Step 3 only
- (d)
Step 4 only
To construct a kite, which of the following is necessary?
- (a)
Two adjacent unequal sides and included diagonal
- (b)
Two adjacent equal sides and included diagonal
- (c)
Length of opposite sides
- (d)
None of these
Which of the following statements is true about the construction of a quadrilateral where AB = 3 cm, BC = 5 cm, AC = 9 cm, AD = 6 cm, CD = 2 cm?
- (a)
It is possible to draw the quadrilateral
- (b)
It is not possible to draw the quadrilateral, since AD + DC < AC
- (c)
It is possible to draw the quadrilateral, since AD + DC < AC
- (d)
None of these
To construct a quadrilateral ABCD, which of the following parts is necessary ?
- (a)
Length of AB
- (b)
Length of BC
- (c)
Measure of ㄥA, ㄥB and ㄥC
- (d)
All of these
Which of the given properties of a parallelogram is necessary to construct it?
- (a)
Opposite sides of a parallelogram
- (b)
Opposite angles of a parallelogram
- (c)
Diagonals of a parallelogram
- (d)
Both (A) and (B)
Arrange the steps of construction while constructing a quadrilateral ABCD given AB = 5.3 cm, AD = 2.9 cm, LA = 70°, ㄥB = 95° and ㄥC = 85°.
Step 1 : With A as centre and radius 2.9 cm, draw an arc to cut AX at D.
Step 2: At B, draw ㄥZBA = 95° so that ZB intersects YD at C.
Step 3: Draw AB = 5.3 cm.
Step 4: At D draw ㄥADY= 110°
Step 5: At A draw ㄥXAB = 70°.
- (a)
3, 4, 2, 1, 5
- (b)
3, 5, 1, 4, 2
- (c)
3, 1, 5, 4, 2
- (d)
3, 5, 4, 2, 1
Match the following:
Column-I | Column-II |
(P) Construction of a quadrilateral can be possible if at least. |
(1) twounequalsides and included diagonal are given. |
(Q) Construction of quadrilateral must satisfy. |
(2) five independent elements are given. |
(R) A kite can be drawn if its | (3) 4 sides,4 angles and 2 diagonals |
(S) A quadrilateral has | (4) triangleinequality and angle sum property of a triangle. |
- (a)
P Q R S 3 2 4 1 - (b)
P Q R S 3 4 2 1 - (c)
P Q R S 2 4 1 3 - (d)
P Q R S 4 3 1 2
Arrange the steps (i) to (iv) in correct order, while constructing a parallelogram ABCD, given \(\bar{AB}\) = 6 cm, \(\bar{AD}\)= 4 cm, and diagonal \(\bar{BD}\)=3cm.
Step 1 : Draw \(\bar{AB}\) = 6 cm
Step (i) : Join \(\bar{AD}\) and \(\bar{BD}\).
Step (ii) : With A as centre, draw an arc of radius 4 cm.
Step (iii) : With Band D as centres and with 4 cm and 6 cm as radii, respectively, draw arcs to cut each other at C.
Step (iv) : With B as centre, draw an arc of radius 3 cm to cut the arc drawn in step (ii) at point D.
Step 6 : Join \(\bar{CD}\) and \(\bar{BC}\). ABCD is the required parallelogram.
- (a)
(ii), (iv), (iii), (i)
- (b)
- (c)
(iii), (ii), (v), (iv)
- (d)
(ii), (iv), (i), (iii)
- (e)
None of these
To construct a convex quadrilateral, which of the following cases is INCORRECT?
- (a)
When the lengths of four sides and one diagonal are given
- (b)
When the lengths of three sides and the two diagonals are given
- (c)
When the lengths of four sides and one angle are given
- (d)
When the lengths of two sides and two included angles are given
Which of the following steps is INCORRECT while constructing a rhombus ABCD, given that AC = 8 cm and BD = 6 cm?
Step 1 : Draw AC = 8 cm.
Step 2 : Draw PQ, the perpendicular of AC. PO intersects AC at point O.
Step 3 : With O as centre and radius equal to 3 cm, drawn an arc cutting OP at D.
Step 4 : With O as centre and radius equal to 3 cm, draw another arc cutting OQ at B.
Step 5 : Join AB, BC, CD and DA.
- (a)
Step 2 only
- (b)
Step 3 only
- (c)
Step 4 only
- (d)
Both Step 2 and Step 5