GM1-9a-Construct.docx
Watch the GCSE Maths videoclip called: Constructing Circles
For constructions, you will need to ensure you have a ruler (or straight edge), sharp pencil, protractor or angle-measurer and a set of compasses. Sometimes you will NOT be allowed to use some of this equipment.
Save and complete ONE of these worksheets: C-6Star, C-EllPatt or C-Flower
IMPORTANT: In order to gain marks…
Distances must be measured accurately to within 2mm.
Angles must be measured/constructed accurately to within 2°.
When ‘constructing’, working lines must be feint BUT MUST remain visible to the examiner and NOT rubbed out!
[NB. A = angle, S = side]
You need to learn how to construct ASA, SAS and SSS triangles.
Watch the GCSE Maths videoclip: Constructing Triangles – From Sides & Angles
SAS Triangles – Given 2 sides and the angle between them
Instructions:
Measure the longest side quoted as the base.
At one end of the line, measure the required angle and put a dot.
Draw a line from that end of the base towards or through the dot, making sure that the length of the line is the length of the smaller line quoted.
Finally join the two measured sides together to form the third side.
Task: Two sides of a triangle are 6cm and 8cm in length. The angle between them is 40°.
On paper, construct this triangle and then answer the questions below.
Q1. What is the length of the third side (to nearest mm)?
Q2. What are the size of the other two angles in your triangle?
………………cm
Measure them accurately. ……………° and ……………°
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GM1-9a-Construct.docx
ASA Triangles – Given 1 sides and the angles at both ends
Instructions:
Measure the side quoted as the base.
Measure one of the angles on the left side, mark it with a dot and draw a feint line from the left side of the base through it.
Measure the other angle on the right side, mark it with a dot and draw a line towards or through it until it reaches the first feint line.
Darken the first feint line up to the meeting point with the last side.
Do NOT rub out the rest of the feint line – it is evidence of your work.
Task: One side of a triangle is 11cm long. It has angles 30° and 45° at each end.
On paper, construct this triangle and then answer the questions below.
Q1. What is the size of the third angle? ………………°
Q2. What are the lengths of the other sides of your triangle?
Measure them to the nearest mm. ……………cm and ……………cm
Watch the GCSE Maths videoclip: Constructing Triangles – From Three Sides
SSS Triangles – You are given all 3 sides but NO angles.
Instructions:
Measure the longest side quoted as the base;
Set your compasses to the 2 nd longest side-length, put the point on the left end of the baseline and then draw an arc.
Set your compasses to the shortest side-length, put the point on the right end of the baseline and then draw an arc that crosses the first arc.
Draw lines from each of the base to where the arcs cross.
Do NOT rub out the arcs – they are evidence of your work.
Task: A triangle has sides that are 5cm, 12cm and 13cm long.
On paper, construct this triangle and then answer the question.
Q1. What are the size of each of the triangle’s angles?
Measure them accurately. ……………°, ……………° and ……………°
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