In the diagram, PQT is a straight line and SQ // RT.
(a) Join QR and show that : (i) < RPS = < QRT ; (ii) < PRS = < QTR. (b) ABC is a triangle. The sides AB and AC are produced to D and E respectively such that < DBC = 132° and < ECD = 96°. Show that ABC is isosceles.
Explanation
(a) < QRT = < RQS (alternate angles) < RPS = < RQS (angles in the same segment) < RPS = < QRT (ii) < QRT = < PQS (corresponding angles) < PQS = < PRS (angles in the same segment) < QTR = < PRS. (b) .
