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Grade 8 · Geometry of 2D Shapes
Congruent & Similar 2D Shapes
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.
- 1.1Two shapes that have the same shape AND the same size are …(1)A)similarB)congruentC)equal in area onlyD)symmetrical
- 1.2Two shapes that have the same shape but DIFFERENT sizes are …(1)A)congruentB)similarC)identicalD)equal
- 1.3In similar triangles, the corresponding ANGLES are …(1)A)doubledB)equalC)halvedD)in the same ratio as the sides
- 1.4△ABC ||| △DEF with AB = 6 cm and DE = 3 cm. The scale factor from △DEF to △ABC is …(1)A)3B)2C)0,5D)18
- 1.5For those triangles, if EF = 5 cm then BC is …(1)A)2,5 cmB)10 cmC)5 cmD)15 cm
- 1.6If the scale factor of an enlargement is 3, the AREA is multiplied by …(1)A)3B)9C)6D)27
- 1.7Which condition proves two triangles CONGRUENT?(1)A)AAAB)SSSC)two angles onlyD)equal areas
- 1.8△ABC ≡ △PQR. The side equal to AC is …(1)A)PQB)PRC)QRD)AB
- 1.9A photograph 6 cm by 4 cm is enlarged so that the longer side becomes 15 cm. The shorter side becomes …(1)A)13 cmB)10 cmC)9 cmD)12 cm
- 1.10Which one of the following is ALWAYS true?(1)A)similar shapes are congruentB)congruent shapes are similarC)all rectangles are similarD)all triangles are similar
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
[14 MARKS]The two right-angled triangles below are similar. The diagrams are not drawn to scale.
- 2.1Calculate the scale factor from the smaller triangle to the larger one.(3)
- 2.2Hence calculate the length of x.(3)
- 2.3Calculate the perimeter of EACH triangle, and show that the perimeters are in the same ratio as the sides.(4)
- 2.4Calculate the area of each triangle and explain why the areas are NOT in the ratio 1,5 : 1.(4)
Question 3
[7 MARKS]Answer the following.
- 3.1Explain the difference between CONGRUENT and SIMILAR shapes.(3)
- 3.2△ABC has sides 4 cm, 6 cm and 7 cm. △PQR has sides 12 cm, 18 cm and 21 cm. Show that the triangles are similar, and write down the scale factor.(4)
TOTAL: 31 marks
This question paper consists of 3 questions.