A trapezium PQRS is such that QR=4cm,PS=8cm angelPQR=105°angelSQR=135°QR//PS.if the height of the trapezium is 5cm use a ruler and a pair of compasses to construct trapezium PQRS
construct a 15° by bisecting a 60° angle twice.
Now you can use that to make the 105° angle
Note that 135 = 90+45. That makes the other angle easy.
To construct trapezium PQRS with the given measurements, follow these steps using a ruler and pair of compasses:
Step 1: Draw a base
Take a ruler and draw a line segment QR of length 4 cm.
Step 2: Draw the top side
From Q, measure and mark a point S on the line extending from QR, such that PS = 8 cm.
Step 3: Draw the height
From point S, draw a perpendicular line segment with a length of 5 cm. Label the point where it intersects QR as T.
Step 4: Complete the trapezium
Connect point T with point P by drawing a line segment TP.
Step 5: Finish the trapezium
Connect point S with point R by drawing a line segment SR. Ensure that SR is parallel to QT.
Your trapezium PQRS is now constructed with the given dimensions and properties.
Note: Step 3 is crucial in constructing the trapezium. It ensures that the height of the trapezium is 5 cm and that QR and PS are parallel.