Everything Maths Grade 10

8.Study the quadrilateralQRSTwith opposite anglesQ^=S^= 117◦and anglesR^=T^= 63◦carefully.

Fill in the correct reasons or steps to prove that the quadrilateralQRSTis a parallelogram.

117 ◦

117 ◦

63 ◦

63 ◦

Q

R S

T

Steps Reasons

? given both\s= 117◦

QRS^ =QT S^ given both\s= 63◦

? sum of\s in quad

RQT^ +QT S^ = 180◦ 117 ◦+ 63◦= 180◦

)QR∥T S co-int\s;QR∥T S

)RS∥QT?

)QRSTis a parallelogram?

9.Study the quadrilateralQRSTwithQ^=S^= 149◦andR^=T^= 31◦carefully. Fill in the correct reasons

or steps to prove that the quadrilateralQRSTis a parallelogram.

149 ◦

149 ◦

31 ◦

31 ◦

Q

R S

T

Steps Reasons

RQT^ =RST^ given both\s= 149◦

QRS^ =QT S^?

Q^+R^+S^+T^= 360◦ sum of\s in quad

RQT^ +QT S^ = 180◦?

? co-int\s;QR∥T S

? co-int\s;RS∥QT

)QRSTis a parallelogram opp. sides are parallel

10.In parallelogramQT RS, the bisectors of the angles have been constructed, indicated with the red lines
below. You are also givenQT=SR,T R=QS,QT∥SR,T R∥QS,Q^=R^andT^=S^.
Prove that the quadrilateralJKLMis a parallelogram.
Note the diagram is drawn to scale.

412 12.2. Chapter summary