Construct a rhombus of perimeter 20cm and one base angle is the supple...
It is given that a rhombus of perimeter 20 cm and one base angle is the supplement of 130 degree
From the given information we get 1 side of rhombus = 20/4 = 5cm
One angle = 130 degree therefore the adjacent angle = 180 - 130 = 50 degree
Drawing of rhombus
Step1: draw a line segment AB of 5 cm
Step 2: Draw line AX from A making an angle of 130 degree with AB and draw a line BY from B making an angleof 50 degree with AB
Step 3: Mark a point on AX as D such that AD = 5cm
Step 4: Mark a point on BY as C such that BC = 5cm
ABCD is arhombus of perimeter 20 cm and one base angle is the supplement of 130 degree
This question is part of UPSC exam. View all Class 8 courses
Construct a rhombus of perimeter 20cm and one base angle is the supple...
Construction of a Rhombus with a Perimeter of 20 cm and one base angle as the supplement of 130 degrees
To construct a rhombus with a perimeter of 20 cm and one base angle as the supplement of 130 degrees, we will follow the steps below:
Step 1: Draw a line segment
Start by drawing a line segment AB of any length. This will be one side of the rhombus.
Step 2: Construct a perpendicular bisector
Construct a perpendicular bisector to AB at point B. This can be done by using a compass and drawing arcs above and below AB.
Step 3: Measure the length of AB
Measure the length of AB to determine the perimeter of the rhombus. In this case, the perimeter is given as 20 cm.
Step 4: Divide the perimeter by 4
Since a rhombus has all four sides equal in length, divide the perimeter (20 cm) by 4 to find the length of each side. In this case, each side of the rhombus will be 5 cm.
Step 5: Construct a parallelogram
Using the measured length of each side (5 cm), construct a parallelogram with sides AB, BC, CD, and DA. This can be done by drawing lines parallel to AB from points C and D.
Step 6: Measure the base angle
Measure the base angle of the rhombus. In this case, the base angle is given as the supplement of 130 degrees. The supplement of an angle is the difference between 180 degrees and the angle itself. So, the base angle would be 180 degrees - 130 degrees = 50 degrees.
Step 7: Construct the remaining sides
Using the measured base angle (50 degrees), construct the remaining sides of the rhombus by drawing lines from points C and D. These lines should be equal in length to the sides AB and AD, and should be at an angle of 50 degrees to AB.
Step 8: Complete the rhombus
Once the remaining sides are constructed, label the points where they intersect with AB as E and F. Connect EF to complete the rhombus.
Step 9: Verify the properties
To verify that the constructed figure is indeed a rhombus, check if all four sides are equal in length (5 cm) and if opposite angles are equal. Also, ensure that the diagonals intersect at right angles and bisect each other.
Conclusion
By following the above steps, a rhombus with a perimeter of 20 cm and one base angle as the supplement of 130 degrees can be constructed. Remember to measure accurately and use the given information to ensure the correct construction.
To make sure you are not studying endlessly, EduRev has designed Class 8 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 8.