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Grade 10 · Euclidean Geometry
Congruent & Similar Triangles (Grade 10)
EXAM-STYLE CLASS TEST
Marks
35
Duration
55 minutes
Questions
3
Name:
Class:
Date:
Mark
/ 35
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 these is NOT a condition for congruency?(1)A)AAAB)SSSC)SASD)RHS
- 1.2Two triangles whose corresponding angles are equal are …(1)A)similarB)congruentC)both similar and congruentD)neither
- 1.3In △ABC and △DEF, AB = DE, ∠B = ∠E and BC = EF. The reason for congruency is …(1)A)SASB)SSSC)AASD)RHS
- 1.4△ABC ∼ △PQR and AB is twice PQ. If BC = 10 then QR = …(1)A)5B)20C)10D)2
- 1.5Two similar triangles have sides in the ratio 3 : 5. Their AREAS are in the ratio …(1)A)9 : 25B)3 : 5C)6 : 10D)27 : 125
- 1.6In congruent triangles △ABC and △PQR, written in that order, the side matching AC is …(1)A)PRB)PQC)QRD)AC
- 1.7RHS can be used only when …(1)A)both triangles have a right angleB)all three sides are knownC)the triangles are similarD)two angles are equal
- 1.8A photo 8 cm by 12 cm is enlarged so that the shorter side becomes 20 cm. The longer side becomes …(1)A)30 cmB)24 cmC)32 cmD)18 cm
- 1.9Congruent triangles are always similar. Similar triangles are …(1)A)not always congruentB)always congruentC)never congruentD)never similar
- 1.10In △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)they share a right angleD)their areas are equal
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
[12 MARKS]In the diagram, △ABC and △DEF are similar, with △ABC ||| △DEF. AB = 6 cm, DE = 4 cm and BC = 9 cm.
- 2.1Write down the scale factor from △DEF to △ABC, and explain what that factor tells you about the two triangles.(3)
- 2.2Calculate the length of EF.(3)
- 2.3State what is true about the corresponding ANGLES of the two triangles, give a reason, and explain why the SIDES cannot also be equal unless the scale factor is 1.(3)
- 2.4Determine the ratio of the AREA of △ABC to the area of △DEF, with a reason.(3)
Question 3
[13 MARKS]Answer the questions below on congruency.
- 3.1Write down the FOUR conditions for two triangles to be congruent.(4)
- 3.2Explain why AAA is NOT a condition for congruency, and name what AAA does prove.(3)
- 3.3Two right-angled triangles have equal hypotenuses and one other pair of equal sides. Name the condition that proves them congruent, and explain why SAS does not apply here.(3)
- 3.4If △ABC ≡ △PQR, write down which side is equal to AC and which angle is equal to B̂, and explain how the order of the letters tells you.(3)
TOTAL: 35 marks
This question paper consists of 3 questions.