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Grade 9 · Geometry of 2D Shapes
Congruent & Similar Triangles: The Four Conditions
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.
- 1.1Which one of the following is NOT a condition for congruency?(1)A)RHSB)SSSC)SASD)AAA
- 1.2△ABC ≡ △DEF means the two triangles are …(1)A)equal in area onlyB)similar onlyC)the same shape AND the same sizeD)the same shape only
- 1.3Which of the following is enough to prove that two triangles are SIMILAR?(1)A)two pairs of sides in the same ratioB)two pairs of equal anglesC)one pair of equal sidesD)one pair of equal angles
- 1.4In △ABC ≡ △PQR, the angle equal to B̂ is …(1)A)R̂B)P̂C)ÂD)Q̂
- 1.5Two triangles have equal hypotenuses and one other pair of equal sides, and both are right-angled. They are congruent by …(1)A)RHSB)SASC)SSSD)AAA
- 1.6Equiangular triangles are always …(1)A)right-angledB)the same sizeC)similarD)congruent
- 1.7△ABC ||| △DEF with AB = 8, DE = 4 and BC = 10. Then EF = …(1)A)20B)5C)10D)2,5
- 1.8In similar triangles, corresponding SIDES are …(1)A)equalB)in the same ratioC)perpendicularD)supplementary
- 1.9Which pair of triangles must be congruent?(1)A)both with the same areaB)both with angles 30°, 60°, 90°C)both with sides 3, 4, 5D)both right-angled
- 1.10A photograph is enlarged by a factor of 4. Its PERIMETER is multiplied by …(1)A)4B)8C)16D)2
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
[11 MARKS]Study the two triangles in the diagram below. The diagrams are not drawn to scale.
- 2.1Write down the condition of congruency that proves △ABC ≡ △DEF, and explain why that condition is enough.(4)
- 2.2Explain why the ORDER of the letters matters when you write △ABC ≡ △DEF.(3)
- 2.3A learner claims that AAA proves two triangles congruent. Explain why the learner is wrong, and state what AAA DOES prove.(4)
Question 3
[10 MARKS]△PQR and △XYZ are similar. PQ = 8 cm, QR = 6 cm and XY = 20 cm. △PQR is right-angled at Q.
- 3.1Calculate the scale factor from △PQR to △XYZ.(3)
- 3.2Hence calculate the length of YZ.(3)
- 3.3Calculate the length of PR, and hence the length of XZ.(4)
TOTAL: 31 marks
This question paper consists of 3 questions.