ACS Jakarta
Mathematics Department
Grade 8
Worksheet 1 – Congruence & Similarity
Name :
Class :
Date :
1.
Each of the following pairs of figures are congruent. Find the values of the unknowns.
2
In the figures below, triangle ABC is similar to triangle APQ. Solve for the unknowns.
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ACS Jakarta
Mathematics Department
3
The length of the sides of hexagon (6-sided polygon) are 9 cm, 11.7 cm, 15 cm, 4.8 cm, 19.2 cm
and 12.3 cm respectively. If the shortest side of a similar hexagon is 1.6 cm, find
a) the lengths of its other sides
b) its perimeter.
4
A tree casts a shadow 10 m long while a 2 m pole casts a shadow 3 m long. How tall is the tree?
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ACS Jakarta
Mathematics Department
5
A line from the top of a cliff to the ground just passes over the top of a telephone pole 6 m high.
The line meets the ground at a point 4.5 m from the base of the pole. If the line is 36 m from this
point to the base of the cliff, how high is the cliff?
6
A hiker walks in a straight line from P to T and stops every 10 km for a rest at Q, R and S. At Q, he
is 6 km further North than he was at P.
How much further North than P is he at
a) R
b) S
c) T
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ACS Jakarta
Mathematics Department
7
A pentagon has sides 4 cm, 5 cm, 6 cm, x cm and 8 cm respectively. A similar pentagon has the
corresponding shortest side 12 cm. Find
a) The longest side of the larger pentagon
b) The value of x if the perimeter of the larger pentagon is 90 cm
c) The ratio of the area of the smaller pentagon to that of the larger pentagon
8
On a scale drawing, the length of a school hall is 10 cm. The actual length of the hall is 50 m.
a) What is the scale used?
b) If the width of the hall is 30 m, find its width on the scale drawing.
9
In the following diagram, PQR is a triangle in which PQ = PR. The side PR is produced to S such
that RS = PR and RQ is produced to T such that TQ = QR. Explain why triangles PTQ and SQR
are congruent.
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