Everything Maths Grade 10

28.The figure below shows△M N Qcrossed byRP. PointsPandRbisect their respective sides of the
triangle.

N M

Q

15 d

P 9 d R

a)The anglesQ^= 15dandRP Q^ = 9dare given in the large triangle; determine the value ofM^ in

terms ofd.

b)You are now told thatRP Q^ has a measure of 60 ◦. Solve for the value ofd. Give your answer as an

exact fractional value.

29.Calculateaandb:

T

R

P

S

Q

a

15

b

4

9

b

30.△P QRand△P SRare equilateral triangles. Prove thatP QRSis a rhombus.

12

匀^12

倀

刀

儀

31.LM N Ois a quadrilateral withLM=LOand diagonals that intersect atSsuch thatM S=SO. Prove
that:

L

N

M S O

a)MLS^ =SLO^

b)△LON△LM N

c)M O?LN

280 7.5. Chapter summary