The Midpoint Theorem (Grade 10) — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 10 · Euclidean Geometry

The Midpoint Theorem (Grade 10)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 12

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
State the midpoint theorem.
(2)
The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.✓✓ (2)
2
D and E are midpoints of AB and AC; BC = 14 cm. Find DE.
(1)
7 cm✓ (1)
3
D and E are midpoints of AB and AC; BC = 25 cm. Find DE.
(1)
12,5 cm✓ (1)
4
D and E are midpoints; DE = 6,5 cm. Find BC.
(1)
13 cm✓ (1)
5
D and E are midpoints; DE = 9 cm. Find BC.
(1)
18 cm✓ (1)
6
State the converse of the midpoint theorem.
(2)
A line through the midpoint of one side, parallel to a second side, bisects the third side.✓✓ (2)
7
D is the midpoint of AB and DE ∥ BC. What can you conclude about E?
(2)
E is the midpoint of AC (converse of the midpoint theorem).✓✓ (2)
8
Why are △ADE and △ABC similar?
(2)
DE ∥ BC gives equal corresponding angles and Â is common, so they are equiangular — and equiangular triangles are similar (AD : AB = AE : AC = 1 : 2).✓✓ (2)

TOTAL: 12 marks