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

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Grade 12 · Euclidean Geometry

Proportionality & Similarity Theorems (Grade 12)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 20

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)
AD/DB = AE/EC (line ∥ one side of △)✓✓ (2)
2
DE ∥ BC with AD = 4, DB = 6 and AE = 5. Calculate EC.
(3)
4/6 = 5/EC → EC = 7,5✓✓✓ (3)
3
In △ABC below with DE ∥ BC, prove that △ADE ||| △ABC.
(4)
Â common; AD̂E = AB̂C and AÊD = AĈB (corresponding ∠s, DE ∥ BC) → △ADE ||| △ABC (AAA)✓✓✓✓ (4)
4
If AD = 4 and DB = 6, write down the length of AB.
(1)
4 + 6 = 10✓ (1)
5
How many pairs of equal angles must you prove for AAA?
(1)
Two — the third follows because the angles of a triangle add to 180°.✓ (1)
6
△ABC ||| △DEF with AB = 8, DE = 12 and BC = 10. Calculate EF.
(3)
8/12 = 10/EF → EF = 15✓✓✓ (3)
7
State the reason you must quote when using the proportion theorem.
(1)
(line ∥ one side of △)✓ (1)
8
Two triangles are equiangular. What can you conclude?
(2)
They are similar, so their corresponding sides are in proportion.✓✓ (2)
9
The sides of △ABC are 4 cm, 6 cm and 8 cm. The sides of △KLM are 6 cm, 9 cm and 12 cm. Are the triangles similar? Give a reason.
(3)
6/4 = 9/6 = 12/8 = 1,5 ✓✓, so the sides are in proportion and the triangles are similar (sides of △ in prop) ✓(3)

TOTAL: 20 marks