Welcome GCSE Maths

Aims for this week Use straight edge and a pair of compasses to do standard constructions. Construct the perpendicular bisector of a given line. Construct the perpendicular from a point to a line. Construct the bisector of a given angle. Construct a triangle. KEYWORDS Construct, circle, arc, vertex, two-dimensional, solid, angles, degree, bisect, perpendicular

PERPENDICULAR BISECTOR Move your compasses to the end of the line Make an arc above and below the line. Repeat from the other end of the line. Draw a line through the two sets of arcs. Finished!! The two lines are at 90° to each other. Check if you like.

THE PERPENDICULAR FROM A POINT TO A LINE Draw a straight line Move your compasses to the point. Draw an arc on the line either side of the point. Move compasses to where the arc goes through the line. Make an arc below the line. Repeat other end of the line. Now draw a line to connect the point and the arc. Finished!! The point is 90° to the line. Check if you like.

ANGLE BISECTOR Move the compass to the meeting point of the lines. Draw an arc on both lines Move the compasses to each of the arcs on the lines in turn. Make another arc in the general area of the bisector, (half way between the lines). Repeat from the other arc. Now draw a line from the end of your line through the arcs. Finished. Check if you like.

THE PERPENDICULAR THROUGH A POINT ON A LINE Move your compasses to the point. Open them up so they can cross over the line. Draw two arcs on the line. Move compasses to one of the arcs. Draw an arc on the other side of the line roughly in the middle. Repeat this from the other arcs. DO NOT CHANGE THE COMPASSES! Now draw a line from the original point to this new crass (only the one line )

Individual constructions Complete the constructions task and stick into books

Reflection of the lesson What did you learn new today? Why did you learn it? How are you going to remember it? Next week… Pythagoras’ theorem

Starter A Draw a circle and mark a point A on its circumference. A B Keep the compasses set at the size of the radius, and from point A draw an arc that cuts the circle at point B. A B Repeat the process until six point are marked on the circumference. Join the points. What shape have you contructed?

Do you remember how to… TASK EXTENSION 1) Construct an perpendicular bisector to the line below: 2) Construct an angle bisector to the angle below: EXTENSION Construct an equilateral triangle with a ruler and compasses. 11

How to Construct a triangle using 3 different methods Vocabulary Compasses Draw Protractor Arc Construct S S S (Side, side, side) S S A (Side, side, angle) S A A (Side angle, angle)

Side, side, side 1. Draw a line approximately 4cm Long and label it AB 2. Set your compasses to 5cm and with the point on A, draw an arc above the line AB. C 5cm 3. Set your compasses to 3cm and with the point on B, scribe an arc above the line AB. Where it crosses the other arc, call this point C 3cm A 4cm B 4. Draw the lines from A to C and B to C to complete the construction. Note this is a special type of triangle. Measure angle B to find out.

Side, side, angle 1. Draw a line approximately 4cm Long and label it AB A 4cm B 2. Set the compasses to 5cm and with the compass point at A, draw an arc above the line AB 3. Place the protractor on the line so that the cross-hairs are over point A and the 0 – 180o line is covering the 4 cm line. Then mark a point at 50o

Side, side, angle continued 4. Remove the protractor and draw a line from A to the point you have just marked at 500 through the arc. Call this point C C 5cm 50o A 4cm B 5. Draw a line from point B to point C

Side, angle, angle 1. Draw a line approximately 4cm Long and label it AB A 4cm B 2. Place the protractor on the line so that the cross-hairs are over point A and the 0 – 180o line is covering the 4 cm line. Then mark a point at 50o in an anticlockwise direction

Side, angle, angle continued… 1. Draw a line approximately 4cm Long and label it AB 50o A 4cm B 2. Place the protractor on the line so that the cross-hairs are over point A and the 0 – 180o line is covering the 4 cm line. Then mark a point at 50o in an anticlockwise direction 3. From A draw a line to the mark just made and mark the angle as 50o 4. Now place the protractor on the line so that the cross-hairs are over point B and the 0 – 180o line is covering the 4 cm line. Then mark a point at 30o in a clockwise direction

Side, angle, angle continued… 4cm B 5. From B draw a line to the mark just made and mark the angle as 30o 6. Finally, where the two lines cross, mark that point C

Tringle construction You need to do at least 2 of each type of triangle. Use the guide to help you. Make sure to label the size of the lengths/angles that you have just drawn.

Reflection of the lesson What did you learn new today? Why did you learn it? How are you going to remember it?