Proportionality & Similarity Theorems (Grade 12) — Worksheet & Memo

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Grade 12 · Euclidean Geometry

Proportionality & Similarity Theorems (Grade 12)

MEMORANDUM

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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
In △ABC below, DE ∥ BC. Write down the proportion that follows, with a reason.
(2)
ADDB = AEEC (line ∥ one side of △)✓✓ (2)
2
DE ∥ BC with AD = 4, DB = 6 and AE = 5. Calculate EC.
(2)
46 = 5EC → EC = 7,5✓✓ (2)
3
In △ABC below with DE ∥ BC, prove that △ADE ||| △ABC.
(2)
Â common; AD̂E = AB̂C and AÊD = AĈB (corresponding ∠s, DE ∥ BC) → △ADE ||| △ABC (AAA)✓✓ (2)
4
If AD = 4 and DB = 6, write down the length of AB.
(2)
4 + 6 = 10✓✓ (2)
5
How many pairs of equal angles must you prove for AAA?
(2)
Two — the third follows because the angles of a triangle add to 180°.✓✓ (2)
6
△ABC ||| △DEF with AB = 8, DE = 12 and BC = 10. Calculate EF.
(2)
812 = 10EF → EF = 15✓✓ (2)
7
State the reason you must quote when using the proportion theorem.
(2)
(line ∥ one side of △)✓✓ (2)
8
Two triangles are equiangular. What can you conclude?
(2)
They are similar, so their corresponding sides are in proportion.✓✓ (2)

TOTAL: 16 marks