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Grade 12 · Euclidean Geometry
Proportionality & Similarity Theorems (Grade 12)
EXAM-STYLE CLASS TEST
Marks
31
Duration
50 minutes
Questions
3
Name:
Class:
Date:
Mark
/ 31
Instructions and Information
- Answer ALL the questions in this question paper.
- Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
- Show ALL calculations clearly.
- Show all units where applicable.
- Number the answers correctly according to the numbering system used in this question paper.
- A non-programmable calculator may be used, unless stated otherwise.
- Write neatly and legibly.
Question 1
[10 MARKS]Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.
- 1.1A line drawn PARALLEL to one side of a triangle divides the other two sides …(1)A)proportionallyB)into equal partsC)at right anglesD)in the ratio 2 : 1
- 1.2In △ABC, D lies on AB and E on AC with DE ∥ BC. If AD = 4, DB = 6 and AE = 6, then EC = …(1)A)9B)4C)6D)15
- 1.3Two triangles are SIMILAR when …(1)A)their corresponding angles are equalB)their corresponding sides are equalC)they have the same areaD)they have the same perimeter
- 1.4If △ABC ∼ △DEF with a scale factor of 3, the ratio of their AREAS is …(1)A)9 : 1B)3 : 1C)27 : 1D)1 : 3
- 1.5In △ABC with ∠B = 90° and BD ⊥ AC, BD² = …(1)A)AD × DCB)AD + DCC)AC × ADD)AB × BC
- 1.6In that same triangle, AB² = …(1)A)AD × ACB)DC × ACC)AD × DCD)AC² − AD²
- 1.7Triangles with the SAME height have areas in the ratio of …(1)A)their basesB)their heightsC)the squares of their basesD)their perimeters
- 1.8In △ABC, D lies on AB and E on AC with DE ∥ BC. △ADE and △ABC are similar because …(1)A)their corresponding angles are equalB)their sides are equalC)their areas are equalD)DE bisects BC
- 1.9The MIDPOINT theorem is the proportion theorem with the special ratio …(1)A)1 : 1B)1 : 2C)2 : 1D)1 : 3
- 1.10Two similar triangles have areas of 16 cm² and 25 cm². Their sides are in the ratio …(1)A)4 : 5B)16 : 25C)2 : 5D)8 : 25
Answer grid — circle your answers for Question 1
| 1.1 | A | B | C | D |
| 1.2 | A | B | C | D |
| 1.3 | A | B | C | D |
| 1.4 | A | B | C | D |
| 1.5 | A | B | C | D |
| 1.6 | A | B | C | D |
| 1.7 | A | B | C | D |
| 1.8 | A | B | C | D |
| 1.9 | A | B | C | D |
| 1.10 | A | B | C | D |
Question 2
[10 MARKS]In △ABC, D lies on AB and E lies on AC, with DE ∥ BC. It is given that AD = 4 cm, DB = 6 cm and AE = 6 cm.
- 2.1State the proportion theorem that applies here, with its reason.(3)
- 2.2Calculate the length of EC.(4)
- 2.3Write down the ratio AD : AB, and hence the ratio DE : BC.(3)
Question 3
[11 MARKS]△PQR ||| △STU, with PQ = 4 cm and ST = 10 cm.
- 3.1Write down the ratio of the corresponding sides.(2)
- 3.2Determine the ratio of the AREA of △PQR to the area of △STU, with a reason.(3)
- 3.3If the area of △STU is 75 cm2, calculate the area of △PQR.(3)
- 3.4Explain why equiangular triangles must be similar.(3)
TOTAL: 31 marks
This question paper consists of 3 questions.