How do you construct a quadrilateral with two pairs of parallel sides of length 4 cm and 6 cm and one pair of opposite angles each measuring 123 degrees
The two sides of different lengths must be adjacent to each other, and the included angle is 123°.
Construct a triangle using 4 and 6 cm as adjacent sides and an included angle of 123°. The missing (third) side of the triangle is the diagonal of the parallelogram. Draw lines parallel to the sides of lengths 4 and 6 cm to complete the figure.
To construct a quadrilateral with the given criteria, follow these steps:
1. Draw a straight line segment AB of length 6 cm.
2. At Point B, use a compass to draw an arc with a radius of 4 cm. Label the point where the arc intersects the line segment as D.
3. From Point D, use a compass to draw another arc with a radius of 6 cm. Label the point where the arc intersects the line segment as C.
4. Draw a straight line segment CD.
5. At Point C, use a compass to draw an arc with a radius of 4 cm. Label the point where the arc intersects the line segment as E.
6. From Point E, use a compass to draw another arc with a radius of 6 cm. Label the point where the arc intersects the line segment as F.
7. Draw a straight line segment EF.
Now, you have a quadrilateral ABCD with two pairs of parallel sides of lengths 4 cm and 6 cm, and one pair of opposite angles measuring 123 degrees.
To construct a quadrilateral with two pairs of parallel sides and specific angle measurements, follow these steps:
1. Draw a line segment of length 4 cm. This will be one side of the quadrilateral.
2. At one end of this line segment, draw a line segment perpendicular to it and of length 6 cm. This will be one of the parallel sides of the quadrilateral.
3. At the other end of the 4 cm line segment, draw another line segment also perpendicular to it and of length 6 cm. This will be the second parallel side of the quadrilateral.
4. From the endpoint of the 4 cm line segment, draw a line segment at an angle of 123 degrees. This will be one of the non-parallel sides of the quadrilateral.
5. From the other endpoint of the 4 cm line segment, draw another line segment at an angle of 123 degrees, but in the opposite direction. This will be the opposite side to the one drawn in the previous step.
6. Connect the open ends of the parallel sides with straight line segments. This will complete the construction of the quadrilateral.
By following these steps, you will have successfully constructed a quadrilateral with two pairs of parallel sides of length 4 cm and 6 cm, and one pair of opposite angles measuring 123 degrees.