Question
Without using set squares or protractor, construct a quadrilateral ABCD in which ∠ BAD = 45° , AD = AB = 6 cm, BC= 3.6 cm and CD=5 cm. Locate the point P on BD which is equidistant from BC and CD.
✓
Answer
Steps of construction:
(i) Draw a line AB = 6 cm.
(ii) Draw a ray making an angle of 45° with AB.
(iii) With a as centre, draw AD = 6 cm on the ray.
(iv) Draw an angle bisector of angle BAD.
(v) With Bas centre cut an arc BC = 3.6 cm on the angle bisector.
(vi) With Das centre cut an arc CD = 5 cm on the angle bisector. ABCD is the required quadrilateral.
(vii) Join BD.
(viii) Draw perpendicular bisectors of CD and BC which meet BD on P. Pis the required point.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Prove that the points $A(-5, 4), B(-1, -2)$ and $C(S, 2)$ are the vertices of an isosceles right-angled triangle. Find the coordinates of D so that ABCD is a square.
→The angle of elevation of a cloud from a point 60m above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the cloud.
Using a graph paper, draw an ogive for the following distribution which shows a record of the width in kilograms of 200 students. <
| Weight | Frequency |
| 40-45 | 5 |
| 45-50 | 17 |
| 50-55 | 22 |
| 55-60 | 45 |
| 60-65 | 51 |
| 65-70 | 31 |
| 70-75 | 20 |
| 75-80 | 9 |
Use your ogive to estimate the following :
(1) The percentage of student weighning 55 kgor more
(2) The weight above the heavist 30% of the student fail
(3) The number of students who are
(a) underweight
(b) overweight
If 55.70 kg considered as sandard weight.
The expression $2x^3 + ax^2 + bx – 2$ leaves remainder $7$ and $0$ when divided by $2x – 3$ and $x + 2$ respectively. Calculate the values of $a$ and $b$
→The difference between the outer curved surface area and the inner curved surface area of a hollow cylinder is $352 cm^2$. If its height is $28 \ cm$ and the volume of material in it is $704 cm^3$; find its external curved surface area.
→Calculate the amount and the compound interest for the following:
Rs. 16,000 at $15 \%$ p.a. in $2 \frac{2}{3}$ years
→Rs. 16,000 at $15 \%$ p.a. in $2 \frac{2}{3}$ years
The angle of elevation of the top of an unfinished tower at a point 150 m from its base is 30°. How much higher must the tower be raised so that its angle of elevation at the same point may be 60°?
Take a graph paper and mark the points P(2, 1), Q(7, 1) and R(7,5). Taking QR as the line of symmetry, obtain and write the co-ordinates of point S.
Construct a right angled triangle PQR, in which ∠Q = 90°, hypotenuse PR = 8 cm and QR = 4.5 cm. Draw bisector of angle PQR and let it meets PR at point t. Prove that T is equidistant from PQ and QR.
Find the coordinate of $O,$ the centre of a circle passing through $A (8 , 12) , B (11 , 3),$ and $C (0 , 14).$ Also , find its radius.
→