Congruence and M1 A1
MEP Jamaica: STRAND I
UNIT 33 Congruence and Similarity: CSEC Revision Test
UNIT 33 Congruence and
Similarity
1.
CSEC Revision Test
The diagram shows the side view of a children's climbing frame.
The frame is symmetrical about DH.
C
D
E
The bars AG, BF and CE are parallel.
Angle HAB = 72°
B
F
I
72˚
(a)
What is the size of angle CBI?
(b)
The bar BH bisects the angle ABI.
(i)
(c)
2.
G
H
A
(1 mark)
What is the size of angle IBH?
(1 mark)
What is the size of angle FHG?
(1 mark)
Name a triangle which is congruent to triangle CBI.
(1 mark)
The sloping sides of a flower bowl are part of a cone as shown.
The radius of the top of the bowl is 10 cm and the radius of the bottom of the bowl is 5 cm. The height of the full cone is 24 cm.
Not to scale
10 cm
5 cm
24 cm
(a)
Calculate the volume of the full cone.
(3 marks)
(b)
By using similar figures, calculate the volume of the flower bowl.
(4 marks)
© CIMT and e-Learning Jamaica
1
UNIT 33 Congruence and Similarity: CSEC Revision Test
MEP Jamaica: STRAND I
UNIT 33 Congruence and
Similarity
CSEC Revision Test
C
3.
1 cm
D
E
2 cm
2 cm
B
A
In the triangle, ABC, DE is parallel to AB, CE = 1 cm and DE = EB = 2 cm .
Calculate:
4.
(a)
the length of AB,
(2 marks)
(b)
the ratio of the area of the triangle ABC to the area of the triangle DEC.
(2 marks)
Triangle PQR is mapped onto triangle STR by an enlargement, centre R.
S
8 cm
Q
5 cm
R
T
20 cm
P
(a)
State the scale factor of the enlargement.
(b)
Write as a fraction the value of
(2 marks)
area of triangle PQR area of triangle STR
(2 marks)
© CIMT and e-Learning Jamaica
2
UNIT 33 Congruence and Similarity: CSEC Revision Test
MEP Jamaica: STRAND I
UNIT 33 Congruence and
Similarity
5.
CSEC Revision Test
Pythagoras wrote about a triangle where
A
AB = 1 unit
BC = 1 unit , and
ˆ = 90°
ABC
(a)
(b)
1
Pythagoras claimed that the length of AC is a rational number.
Was he correct? Explain your answer.
B
1
C
ˆ = 90°
UNIT 33 Congruence and Similarity: CSEC Revision Test
UNIT 33 Congruence and
Similarity
1.
CSEC Revision Test
The diagram shows the side view of a children's climbing frame.
The frame is symmetrical about DH.
C
D
E
The bars AG, BF and CE are parallel.
Angle HAB = 72°
B
F
I
72˚
(a)
What is the size of angle CBI?
(b)
The bar BH bisects the angle ABI.
(i)
(c)
2.
G
H
A
(1 mark)
What is the size of angle IBH?
(1 mark)
What is the size of angle FHG?
(1 mark)
Name a triangle which is congruent to triangle CBI.
(1 mark)
The sloping sides of a flower bowl are part of a cone as shown.
The radius of the top of the bowl is 10 cm and the radius of the bottom of the bowl is 5 cm. The height of the full cone is 24 cm.
Not to scale
10 cm
5 cm
24 cm
(a)
Calculate the volume of the full cone.
(3 marks)
(b)
By using similar figures, calculate the volume of the flower bowl.
(4 marks)
© CIMT and e-Learning Jamaica
1
UNIT 33 Congruence and Similarity: CSEC Revision Test
MEP Jamaica: STRAND I
UNIT 33 Congruence and
Similarity
CSEC Revision Test
C
3.
1 cm
D
E
2 cm
2 cm
B
A
In the triangle, ABC, DE is parallel to AB, CE = 1 cm and DE = EB = 2 cm .
Calculate:
4.
(a)
the length of AB,
(2 marks)
(b)
the ratio of the area of the triangle ABC to the area of the triangle DEC.
(2 marks)
Triangle PQR is mapped onto triangle STR by an enlargement, centre R.
S
8 cm
Q
5 cm
R
T
20 cm
P
(a)
State the scale factor of the enlargement.
(b)
Write as a fraction the value of
(2 marks)
area of triangle PQR area of triangle STR
(2 marks)
© CIMT and e-Learning Jamaica
2
UNIT 33 Congruence and Similarity: CSEC Revision Test
MEP Jamaica: STRAND I
UNIT 33 Congruence and
Similarity
5.
CSEC Revision Test
Pythagoras wrote about a triangle where
A
AB = 1 unit
BC = 1 unit , and
ˆ = 90°
ABC
(a)
(b)
1
Pythagoras claimed that the length of AC is a rational number.
Was he correct? Explain your answer.
B
1
C
ˆ = 90°