Congruent & Similar Triangles: The Four Conditions — Worksheet & Memo

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Grade 9 · Geometry of 2D Shapes

Congruent & Similar Triangles: The Four Conditions

MEMORANDUM

Name:

Class:

Date:

Mark

/ 16

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
Name the four conditions for congruent triangles.
(2)
SSS, SAS, AAS and RHS✓✓ (2)
2
Why is AAA not a congruency condition?
(2)
Equal angles fix only the shape, not the size — that gives similarity, not congruency.✓✓ (2)
3
In SAS, where must the equal angle be?
(2)
Between the two equal sides (the included angle).✓✓ (2)
4
Which condition applies only to right-angled triangles?
(2)
RHS✓✓ (2)
5
If △ABC ≡ △PQR, which side equals BC?
(2)
QR (B pairs with Q and C with R)✓✓ (2)
6
If △ABC ≡ △PQR, which angle equals ∠A?
(2)
∠P✓✓ (2)
7
Two similar triangles: AB = 3, DE = 9, BC = 4. Find EF.
(2)
Scale factor 3 → EF = 12✓✓ (2)
8
Two similar triangles have sides 6, 8 and 9, 12. Are they similar? Give the factor.
(2)
9÷6 = 1,5 and 12÷8 = 1,5 → Yes, factor 1,5✓✓ (2)

TOTAL: 16 marks