Everything Maths Grade 10

P

Q R

T S

(^21)
1 2
4.Study the quadrilateralABCDwith opposite anglesA^=C^= 108◦and anglesB^=D^= 72◦carefully.
Fill in the missing reasons and steps to prove that the quadrilateralABCDis a parallelogram.
108 ◦
108 ◦
72 ◦
72 ◦
A
B C
D
Steps Reasons
? given both\’s = 108◦
ABC^ =ADC^ given both\’s= 72◦
A^+B^+C^+D^= 360◦ sum of\s in quad
BAD^ +ADC^ = 180◦ given 108 ◦+ 72◦= 180◦
)AB∥DC?
)BC∥AD?
)ABCDis a parallelogram opp sides of quad∥
5.Study the quadrilateralQRSTwith opposite anglesQ=S= 124◦and anglesR=T= 56◦carefully.
Fill in the missing reasons and steps to prove that the quadrilateralQRSTis a parallelogram.
124 ◦
124 ◦
56 ◦
56 ◦
Q
R S
T
Steps Reasons
RQT^ =RST^ given both\s= 124◦
? given both\s= 56◦
Q^+R^+S^+T^= 360◦?
RQT^ +QT S^ = 180◦?
)QR∥T S co-int\s;QR∥T S
)RS∥QT co-int\s;RS∥QT
? opp sides of quad ∥

6. a)QuadrilateralQRSTwith sidesQR∥T SandQT∥RSis given. You are also given that:Q^=y
   andS^= 34◦;QT R^ =xandRT S^ = 41◦. Prove thatQRSTis a parallelogram.

406 12.1. Proofs and conjectures