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°.
Related questions
Question
Transcribed Image Text: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
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