Construct a qadilateral abcd, given that ab=4cm , cd=4.5cm,ad=5cm,angle a=70degree and angle d=12odegree
To construct the quadrilateral ABCD, you will need a ruler, a protractor, and a compass. Follow the steps below:
1. Draw a line segment AB of length 4 cm using a ruler.
2. Place the sharp end of your compass at point A and draw an arc with a radius of 5 cm to intersect line AB. Label this intersection point as E.
3. Draw a line segment ED of length 4.5 cm using a ruler, starting from point E in the direction opposite to point A.
4. Place the sharp end of your compass at point E and draw an arc with a radius of 4 cm to intersect line ED. Label this intersection point as C.
5. With the sharp end of your compass at point C, draw an arc with a radius of 5 cm to intersect line segment AB. Label this intersection point as F.
6. Connect points B and C with a straight line segment BC.
7. Connect points D and F with a straight line segment DF to complete the quadrilateral.
8. Finally, use a protractor to measure and mark a 70-degree angle at point A (angle DAB) and a 120-degree angle at point D (angle BCD) to adjust the angles accordingly.
Note: Since the given angles of A and D are not consistent with the side lengths, the construction may not be exact. Make sure to double-check your measurements and adjust as necessary.
Hint -- it will look kind of like an arrowhead.
Draw a horizontal line ab, length 4
Construct angle a = 70°
Draw ad, length 5
Construct angle d = 12°
Now draw a circle of radius 4.5, center at b. It will intersect the line coming down from d. That will be point c.