Congruent & Similar 2D Shapes — Worksheet & Memo

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Grade 8 · Geometry of 2D Shapes

Congruent & Similar 2D Shapes

MEMORANDUM

Name:

Class:

Date:

Mark

/ 14

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
What does it mean if two shapes are congruent?
(2)
Same shape and same size — identical.✓✓ (2)
2
What does it mean if two shapes are similar?
(2)
Same shape, not necessarily the same size: equal angles and all matching sides in the same ratio — congruent shapes are the special case with scale factor 1.✓✓ (2)
3
Are all congruent shapes also similar?
(1)
Yes — with a scale factor of 1.✓ (1)
4
Are all similar shapes congruent?
(1)
No — only when the scale factor is 1.✓ (1)
5
Two similar triangles: sides 5 cm and 8 cm; the matching side to 5 is 15 cm. Find the other.
(2)
Scale factor 3 → 8 × 3 = 24 cm✓✓ (2)
6
A rectangle 4 cm × 6 cm is enlarged by scale factor 2. What are the new sides?
(2)
8 cm × 12 cm✓✓ (2)
7
Triangle A has sides 3, 4 and 5. Triangle B has sides 9, 12 and 15. Are they similar?
(2)
9 ÷ 3 = 3, 12 ÷ 4 = 3 and 15 ÷ 5 = 3 → Yes: all three pairs of sides are in the same ratio (scale factor 3).✓✓ (2)
8
Right-angled triangle A has legs 2 and 4. Right-angled triangle B has legs 6 and 10. Are they similar?
(2)
6 ÷ 2 = 3 but 10 ÷ 4 = 2,5 → No: the sides are not all in the same ratio.✓✓ (2)

TOTAL: 14 marks