Congruent & Similar Triangles (Grade 10) — Worksheet & Memo

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Grade 10 · Euclidean Geometry

Congruent & Similar Triangles (Grade 10)

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
State the four conditions for congruency.
(2)
SSS, SAS, AAS and RHS✓✓ (2)
2
In △ABC and △DEF, AB = DE, BC = EF and CA = FD. Prove that the triangles are congruent.
(2)
All three pairs of sides are equal (given), so △ABC ≡ △DEF (SSS)✓✓ (2)
3
Explain why SSA is not a valid congruency condition.
(2)
Two sides with a non-included angle can produce two different triangles, so it does not fix the triangle.✓✓ (2)
4
What is the difference between congruent and similar triangles?
(2)
Congruent = same shape and same size; similar = same shape, sides in proportion.✓✓ (2)
5
△ABC ||| △DEF with AB = 6, DE = 9 and BC = 8. Calculate EF.
(2)
69 = 8EF → EF = 12✓✓ (2)
6
Two triangles have all three angles equal. Are they congruent?
(2)
No — they are similar. Equal angles fix the shape but not the size.✓✓ (2)
7
Which condition uses a right angle, the hypotenuse and one other side?
(2)
RHS✓✓ (2)
8
In SAS, where must the angle be?
(2)
Between the two given sides (the included angle).✓✓ (2)

TOTAL: 16 marks