Chapter 5 TRANSFORMATIONS

CHAPTER 5 : CONGRUENCY, ENLARGEMENT & COMBINED TRANSFORMATIONS

A. CONGRUENCY AND SIMILARITY
1. Give the definition of
(a) Congruency :
(b) Similarity :
2. Determine whether each of the following pairs are congruent or similar or not.

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Characteristics of triangle congruency - Textbook page 128
3. The diagram show two triangles, ABC and PQR, which is congruent.

Complete the table below. Details
Properties of triangle congruency
Side – Side – Side 2
(SSS)

Angle – Angle – Angle
(AAA)

Side – Side – Angle
(SSA)

Angle – Angle – Side
(AAS)

Side – Angle – Side
(SAS)

Angle – Side – Angle
(ASA)

4. The diagram show two triangles. Is it pair of triangles are congruent?

5. In the diagram, triangle JKL is an image of triangle DEF under a certain reflection.
Find the value of x and y

6. The diagram shows two similar quadrilateral, ABCD and PQRS.
(a) Which side in PQRS is corresponding to side AB in ABCD?
(b) Which angle in PQRS is corresponding to the ∠CDA in ABCD?

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7. The diagrams show a pair of similar shape. Find the value of x

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DO YOU REMEMBER?

1. Mark the image of A under 2. Draw the image of B under 3. Draw the image of C under a
3 −4 reflection at x-axis.
translation −4 translation −6

4. Point D is going under 90˚ 5. Draw the image of E under a 6. F is going under 180˚ rotations

clockwise rotations about (–2, 1). 90˚ anti- clockwise rotation about about the origin. Draw its image.
Mark D’.
point A.

Describe the following transformations.

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B. ENLARGEMENT

1. Find the image of point A under the following enlargement. 1
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a. Enlargement with scale factor 2 about point B. b.Enlargement with scale factor about point C.

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c. Enlargement with scale factor 3 about point D d. Enlargement with scale factor 2 about point E

e. Enlargement with scale factor about the origin f. Enlargement with scale factor – 2 about point (–3, –4)

2. Draw the image of the objects under the following enlargement.
a.Enlargement with scale factor 3 about point x. b. Enlargement with scale factor 2 about point y.

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c Enlargement with centre A and scale factor 1 d. Enlargement with scale factor 2 about point P.
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e. Enlargement with centre N and scale factor 1 f. Enlargement with scale factor -1 about point O.
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3. Diagrams shows an object and its image under a certain enlargement. Mark X as a centre of the enlargement.
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4. Find the scale factor for each enlargement.

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5. The diagrams show the object and its image under a certain enlargement. Describe the enlargement.

6. Calculate the area of the image for the enlargement that have certain area of object & scale factor.

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7. The diagrams show the object and its image under a certain enlargement

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C. COMBINED TRANSFORMATIONS
1. The diagram shows point W and point M drawn in a Cartesian plane.

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2. The diagram shows a triangle TUV.

3. The diagram shows three congurents triangle ABC, PQR and JKL. PQR is an image of ABC under the
transformation V. JKL is an image of PQR under the transformation W. Describe in full :
a) transformation of V
b) transformation of W

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4. The diagram shows three congurent trapezium ABCD, EFGH and JKLM. EFGH is an image of JKLM
under transformation P and ABCD is the image of EFGH under transformation Q. Describe in full
transformation :
a) P :
b) Q :

5. The diagram shows three congurent triangle ABO, BCO and DEO. Describe in full the transformation
of X and Y.

a) X
b) Y

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6. JGLM is the image of DEFG under a transformation U.
ABCD is the image of JGLM under a transformation V.
a) Describe in full of transformation U and V.
U:
V:
b) Given that the area of DEFG is 10 cm2 .

Find the area of JGLM.

7. The diagram shows triangles TUQ, MPN and JKL. TUQ is an image of JKL
under the transformation Q followed by another transformation R.
Describe in full :
a) transformation Q
b) transformation R

c) Given that the area of TUQ is 180 unit² . Find the area of JKL.

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8. The diagram shows three polygons PQRS, TUVW and TCAB.
a) PQRS is an image of TABC under a combined transformation NM.
Describe in full of transformation M and N.
M:
N:

b) If the area polygon PQRS is 6 unit² .
Find the area of shaded region.

9. The diagram show three polygon PQRS, RTUV and RWXY. RWXY is an image of PQRS under the
combined transformation ED.
a) Describe in full :
D:
E:
b) Given that the area of the shaded region is 64 cm² .

Find the area of PQRS.

10. The diagram show quadrilaterals ABCD and CEFG.
ABCD is an image of CEFG under combined transformation PQ.

a) Describe in full :

Q:
P:

c) Given that the area of quadrilateral CEFG is 10 cm² .
Find the area of quadrilateral ABCD.

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11. Given that the polygon PQRSB is an image of polygon ABCDE
under combined transformation MN.
a) Describe in full :
N:
M:

b) Given that the area of shaded region is 132 cm² .
Find the area of polygon ABCDE.

12. PQRS is the image of ABCD under transformation MN.
a) Describe in full of transformation M and N.
N:

M:
b) Given that the area of PQRS is 200 cm² .
Find the area of ABCD.

13. Given that the polygon PQRST is an image of polygon ABCDE under the
combined transformation AB.
a) Describe in full :

B:

A:

b) Given that the area of polygon ABCDE is 4 unit² .
Find the area of polygon PQRST.

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