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WorkSHEET 7.2 Congruence and transformations Name: ___________________________

1 Determine whether the triangles below are

congruent (≡) or not congruent. If the triangles are congruent, write the triangles according to the congruent vertices. For example, ∆AFL ≡ ∆CIO. Give a reason if the triangles are congruent. (a)

(b)

(c)

Answers: (a) ∆ABC ≡ ∆FDE (SSS) (b) Not congruent (c) ∆MON ≡ ∆QPR (ASA)

WorkSHEET 7.2 Congruence and transformations

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2 Identify the congruent triangles and explain why they are congruent. Then, find the values of the pronumerals.

b

c

a

65

B D

AC

Answers: ∆ACB ≡ ∆BDA (RHS) a = 25° (angles add to 180°) ∠CAB ≡ ∠DBA, therefore c = 25° ∠BAD ≡ ∠ABC, therefore b = 65°

3 Identify the congruent triangles and explain why they are congruent. Then, find the values of the pronumerals.

ba

B C

A

D

Answers: ∆ADB ≡ ∆CDB (SSS) ∠ADB ≡ ∠CDB and ∠ADB + ∠CDB = 180° (straight line), therefore a = b = 90°

4 Identify the congruent triangles, and then calculate the values of angles a and b and side c. ABCD is a parallelogram and BD is the diagonal.

Answers: a = 60° (angles in a triangle add to 180°) AD ≡ BC (opposite sides of a parallelogram) BD ≡ ED (given) ∠CBD ≡ ∠EDA (given) ∆ADE ≡ ∆CBD (SAS) ∠AED ≡ ∠CDB, therefore b = 88° AE ≡ CD, therefore c = CD = 10.5 cm (opposite sides of a parallelogram)

WorkSHEET 7.2 Congruence and transformations

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5 Name the following quadrilaterals and give reasons to explain your answer. (a)

(b)

(c)

(d)

Answers: (a) Parallelogram, opposite sides are equal,

opposite angles are equal, two pairs of parallel sides

(b) Square, all sides equal, all angles 90° (c) Kite, two pairs of equal adjacent sides,

one pair of opposite angles equal (d) Trapezium, one pair of parallel sides

WorkSHEET 7.2 Congruence and transformations

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6 Mark all axes of symmetry on this rhombus.

Answer:

Two axes of symmetry.

7 If WXYZ is a rhombus, identify any pairs of congruent triangles.

G

W

XZ

Y

Answers: ∆WXY≡ ∆WZY (SSS) ∆WZX≡ ∆WZX (SSS) ∆ZWG ≡ ∆XWG ≡ ∆XYG ≡ ∆ZYG (ASA)

WorkSHEET 7.2 Congruence and transformations

© John Wiley & Sons Australia, Ltd 5

8 If ABCD is a kite, identify any pairs of congruent triangles.

EC

B

A

D

Answers: ∆ABE ≡ ∆CBE (SSS) ∆ADE ≡ ∆CDE (SSS) ∆ABD ≡ ∆CBD (SSS)

9 Are the following statements true or false?

(a) Angles a and d are alternate. (b) Angles c and f are corresponding. (c) Angles b and f are co-interior.

Answers: (a) True (b) False (they are vertically opposite angles) (c) False (they are corresponding angles)

10 Use congruent triangles to show that a parallelogram with one right angle is a rectangle. A

D C

B

Answer: ∠ABD ≡ ∠CDB (alternate) ∠ADB ≡ ∠CBD (alternate) BD is common to both triangles. ∆ABD ≡ ∆CDB (ASA) ∠DAB ≡ ∠BCD = 90° As ∠DAB and ∠ABC are co-interior, ∠ABC = 90°. Similarly, ∠ADC = 90°. As all angles are 90°, and ABCD is a quadrilateral, it is also a rectangle.