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Grade 10 · Euclidean Geometry
The Midpoint Theorem (Grade 10)
EXAM-STYLE CLASS TEST
Marks
34
Duration
55 minutes
Questions
3
Name:
Class:
Date:
Mark
/ 34
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.
- 1.1In △ABC, D is the midpoint of AB and E the midpoint of AC. Then DE …(1)A)is parallel to BC and half its lengthB)is parallel to BC and equal to itC)is perpendicular to BCD)bisects BC
- 1.2In △PQR, X and Y are the midpoints of PQ and PR. If QR = 18 cm then XY = …(1)A)9 cmB)36 cmC)18 cmD)6 cm
- 1.3In △ABC, D is the midpoint of AB and DE ∥ BC with E on AC. Then E is …(1)A)the midpoint of ACB)any point on ACC)the point where AC = BCD)one third of the way along AC
- 1.4In △ABC, DE joins the midpoints of AB and AC and DE = 7 cm. Then BC = …(1)A)14 cmB)3,5 cmC)7 cmD)21 cm
- 1.5△ABC has perimeter 36 cm. The triangle formed by joining all three midpoints has perimeter …(1)A)18 cmB)12 cmC)9 cmD)36 cm
- 1.6In △ABC, DE joins the midpoints of AB and AC. Then △ADE and △ABC are …(1)A)similar, with sides in the ratio 1 : 2B)congruentC)similar, with sides in the ratio 1 : 4D)not related at all
- 1.7In △ABC, DE joins the midpoints of AB and AC. If △ADE has area 5 cm² then △ABC has area …(1)A)20 cm²B)10 cm²C)15 cm²D)25 cm²
- 1.8In trapezium ABCD with AB ∥ DC and AB longer than DC, the segment joining the midpoints of AD and BC is …(1)A)half the SUM of AB and DCB)half the DIFFERENCE of AB and DCC)equal to ABD)equal to DC
- 1.9In △ABC, AB = 10 and AC = 16. D is the midpoint of AB and DE ∥ BC with E on AC. Then AE = …(1)A)8B)5C)16D)10
- 1.10Why is the midpoint theorem so useful inside a proof?(1)A)it gives a parallel line AND a length in one stepB)it proves two triangles congruentC)it finds the area of a triangleD)it proves a quadrilateral is a rhombus
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
[9 MARKS]In △ABC, D is the midpoint of AB and E is the midpoint of AC. BC = 18 cm.
- 2.1Calculate the length of DE, and give a reason.(3)
- 2.2Write down the relationship between DE and BC other than their lengths, give a reason, and hence state what kind of quadrilateral DBCE is, with a reason.(3)
- 2.3In a different triangle, the line joining the midpoints of two sides is 7,5 cm long. Calculate the length of the third side.(3)
Question 3
[15 MARKS]In △PQR, S is the midpoint of PQ and ST ∥ QR, with T on PR.
- 3.1Prove that T is the midpoint of PR.(4)
- 3.2If QR = 24 cm, calculate the length of ST, giving a reason for the ratio you use.(3)
- 3.3If the perimeter of △PQR is 60 cm, determine the perimeter of △PST.(4)
- 3.4State what happens to the AREA of △PST compared with △PQR, give a reason, and hence calculate the area of quadrilateral STRQ if the area of △PQR is 96 cm2.(4)
TOTAL: 34 marks
This question paper consists of 3 questions.