EXERCISE 1 (Revision) (a) In the diagram, ABCG||FD, ABCG LGH The reflex angle BFE =200° and CGD=50°. Calculate the size of all angles (1) indicated by small letters. (2) Show that DF LFE. 2009 E 2a-50° B 50% ☑18 G H D A E B (b) (1) In AABC, EF||BC. BA is produced to D. Calculate a and hence show that AE = AF. 5a-40° b 2a 80% (2) Calculate, with reasons, the value of b, c, d and e. 165 (c) In the diagram, CD||EF, DEF=28°, ABD=48° and BDE 160°. Prove that AB||CD. A B 489 160° C D E F U (d) In the diagram, PU||QT, T=42°, RQS=82°, PQT=y, UPT=x and QPT=x+40°. x+40° T 42° (1) (2) Prove that PT||QS. Calculate y. 82° S (e) ABCD is a parallelogram, AABE is equilateral and ADEC is isosceles. (1) Show that AE LED (2) Show that ED bisects D B E (f) In the diagram, AB=7 cm, AD=12 cm, 20 cm CE=8 cm and DE=17 cm. 7 cm 17 cm Calculate the length of BC. B B C 8 cm E (g) ABCD is a kite in which AB AD and BC=CD. Prove that: (1) AABC = AADC (2) Why is B=D? (h) AB DE and DC=CB. A B Prove that: (1) AC=CE (2) AB=DE (i) Prove that AABC AADC using two different conditions of congruency. (j) In the figure below, sides PR and QS of triangles PQR and SQR intersect at T. PQ-SR and P=S=90°. Prove that APQR = ASRQ. 166 B E S T R

EXERCISE 1 (Revision) (a) In the diagram, ABCG||FD, ABCG LGH The reflex angle BFE =200° and CGD=50°. Calculate the size of all angles (1) indicated by small letters. (2) Show that DF LFE. 2009 E 2a-50° B 50% ☑18 G H D A E B (b) (1) In AABC, EF||BC. BA is produced to D. Calculate a and hence show that AE = AF. 5a-40° b 2a 80% (2) Calculate, with reasons, the value of b, c, d and e. 165 (c) In the diagram, CD||EF, DEF=28°, ABD=48° and BDE 160°. Prove that AB||CD. A B 489 160° C D E F U (d) In the diagram, PU||QT, T=42°, RQS=82°, PQT=y, UPT=x and QPT=x+40°. x+40° T 42° (1) (2) Prove that PT||QS. Calculate y. 82° S (e) ABCD is a parallelogram, AABE is equilateral and ADEC is isosceles. (1) Show that AE LED (2) Show that ED bisects D B E (f) In the diagram, AB=7 cm, AD=12 cm, 20 cm CE=8 cm and DE=17 cm. 7 cm 17 cm Calculate the length of BC. B B C 8 cm E (g) ABCD is a kite in which AB AD and BC=CD. Prove that: (1) AABC = AADC (2) Why is B=D? (h) AB DE and DC=CB. A B Prove that: (1) AC=CE (2) AB=DE (i) Prove that AABC AADC using two different conditions of congruency. (j) In the figure below, sides PR and QS of triangles PQR and SQR intersect at T. PQ-SR and P=S=90°. Prove that APQR = ASRQ. 166 B E S T R

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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