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 (Delta) ABC is isosceles.
Explanation
(a) < QRT = < RQS (alternate angles)
< RPS = < RQS (angles in the same segment)
(therefore) < RPS = < QRT
(ii) < QRT = < PQS (corresponding angles)
< PQS = < PRS (angles in the same segment)
(therefore) < QTR = < PRS.
(b) (< ABC = hat{B} = 180° – 132° = 48°)
(< ACB = hat{C} = 180° – 96° = 84°)
(< BAC = hat{A} = 180° – (48° + 84°) = 48°)
(< BAC = < ABC = 48°)
(therefore Delta ABC = isosceles).