Everything Maths Grade 10

32.Using the figure below, show that the sum of the three angles in a triangle is 180°. LineDEis parallel
toBC.

B C

D A E

a

b c

d e

33.P QRis an isosceles triangle withP R=QR.Sis the mid-point ofP Q,Tis the mid-point ofP RandU
is the mid-point ofRQ.

P S Q

R

T U

a)Prove△ST Uis also isosceles.

b)What type of quadrilateral isST RU? Motivate your answer.

c)IfRT U^ = 68°calculate, with reasons, the size ofTSU^.

34.ABCDis a parallelogram.BE=BC. Prove thatABE^ =BCD^.

A B

D E C

35.In the diagram below,D,EandGare the mid-points ofAC,ABandBCrespectively.EC∥F G.

Chapter 7. Euclidean geometry 281