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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 equal to itB)bisects BCC)is parallel to BC and half its lengthD)is perpendicular to BC
- 1.2In △PQR, X and Y are the midpoints of PQ and PR. If QR = 18 cm then XY = …(1)A)36 cmB)9 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)any point on ACB)one third of the way along ACC)the point where AC = BCD)the midpoint of 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)21 cmD)7 cm
- 1.5△ABC has perimeter 36 cm. The triangle formed by joining all three midpoints has perimeter …(1)A)9 cmB)36 cmC)12 cmD)18 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)not related at allC)congruentD)similar, with sides in the ratio 1 : 4
- 1.7In △ABC, DE joins the midpoints of AB and AC. If △ADE has area 5 cm² then △ABC has area …(1)A)25 cm²B)15 cm²C)10 cm²D)20 cm²
- 1.8In △ABC, D is the midpoint of AB, and the line through D parallel to BC meets AC at E. Which statement is TRUE?(1)A)E is the midpoint of ACB)DE = BCC)AE = EC = BCD)DE ∥ AB
- 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)10D)16
- 1.10Why is the midpoint theorem so useful inside a proof?(1)A)it proves a quadrilateral is a rhombusB)it finds the area of a triangleC)it gives a parallel line AND a length in one stepD)it proves two triangles congruent
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.