Mathematics Constructions

Aims of the Lesson To learn how to construct triangles. To learn how to bisect lines at right angles. To learn how to bisect angles.

Triangles The types of constructions are denoted using S to stand for side and A to stand for angle. SAS means you are given two side lengths and the angle between them. ASA means you are given the base’s length and the angle at each end of it. SSS means you are given all three sides (but no angles)

SAS Triangles Draw the longest side (using a ruler). At one end of the base, measure the angle given (using a protractor). Draw a line at this angle, equal to the length of the other side quoted (using a ruler). Now join the other end of the base line to the other end of this second side (using a ruler).

SAS Triangles STEP 4: Now join the other end of the base line to the other end of this second side (using a ruler). STEP 3: Draw a line at this angle, equal to the length of the other side quoted (using a ruler). STEP 1: Draw the longest side (using a ruler). STEP 2: At one end of the base, measure the angle given (using a protractor).

ASA Triangles Draw the side given as the base (using a ruler). At one end measure one of the angles. Draw a LONG FEINT line at this angle. At the other end, measure the other angle. Draw a line at this angle that meets the feint line you just drew. Now darken the other side’s line from the base to the third side (but do NOT rub out the rest of the feint line – these are your workings/construction lines!)

ASA Triangles STEP 2: At one end measure one of the angles. STEP 6: Now darken the other side’s line from the base to the third side (but do NOT rub out the rest of the feint line – these are your workings/construction lines!) STEP 5: Draw a line at this angle that meets the feint line you just drew. STEP 3: Draw a LONG FEINT line at this angle. STEP 4: At the other end, measure the other angle. STEP 1: Draw the side given as the base (using a ruler).

SSS Triangles STEP 4: Finally, draw lines from each end of the base to the cross-over point of the arcs, but do NOT rub out your arc lines – these are your workings/ construction lines! STEP 1: Draw the longest side (using a ruler). STEP 2: Set the compasses to the length of the second side, put the point at one end of the base and draw a feint long arc. STEP 3: Now set the compasses to the length of the third side, put the point at the other end of the base and draw a feint arc to cross the first arc.

What is a perpendicular bisector? A bisector cuts something into 2 (bi) equal sections (sector); Perpendicular means at right angles; Therefore a perpendicular bisector is a line that cuts the original line into 2 equal halves, and also crosses it at 90°

Perpendicular Bisectors You will be given a line. Set your compass so that they are equal to about ¾ of the length of the line. Put the point of the compass at one end of the line and draw a feint arc above and below the line.

Perpendicular Bisectors Put the point of the compass at the other end of the line and draw feint arcs which cross over the previous two arcs. Now draw a straight line through both cross-over points (but do NOT rub out your arcs). This line is at right angles to the original line and cuts the original line in half – perpendicular bisector!

What is an angle bisector? A bisector cuts something into 2 (bi) equal sections (sector); Therefore an angle bisector is a line that cuts the original angle into 2 equal halves.

Angle Bisector You will be given an angle between two lines. Set your compasses at a length of about 3-4cm Put the point of the compass at the point of the angle and draw an arc through each line forming the angle.

Angle Bisector Put the point of the compass at each of these cross-over points and draw an arc from each which cross-over each other. Now draw a line from the original angle’s point through the last cross-over point (but do NOT rub out any of your arcs). This line has cut the original angle in half and is therefore the angle bisector!

What next? Print out the notes called Shape4. Read through them and make sure you answer any questions. Work through the MyMaths lesson and then its online homework called: Shape > Constructions > Constructing Triangles found at: http://app.mymaths.co.uk/276-resource/constructing-triangles http://app.mymaths.co.uk/276-homework/constructing-triangles You have now completed this module of work. Revise and then ask your teacher to email you the assessment to complete and return via email to your VLE teacher.