Euclid 1 Find the point X where the lines joining A to B and C to D cross.

B

● DA

●C

Find the point Y where the lines joining A to C and B to D cross.

●

●

Make up more problems like this and solve them.

Euclid 2

●

Copy segment AB to line L starting at C.

C

B

A

L

Make up more problems like this and solve them.

●D

M

Create segment DZ twice as long as AB starting at D on line M.

Make a copy of triangle ABC.

C

BA

Euclid 3

Make up more triangles and copy them.

Make a triangle with these three sides.

Euclid 4

Make a triangle with these three sides.

Make up more problems like this and solve them.

Make two or three different quadrilaterals with these four sides.

Euclid 5

Make up more problems like this and solve them.

Euclid 6 Find the right place for C so that ABC is an equilateral triangle.

B

A

Make up more problems like this and solve them.

C

Euclid 7 Find the point X that divides segment AB in half.

Remember – no measuring!

Ask for a hint if you need one.

B

A

Make up more problems like this and solve them.

Find the midpoints X, Y and Z of the sides of triangle ABC. Then draw AX, BY and CZ.

What do you notice?C

BA

Euclid 8

Try this with some other triangles.

X

Y

Z

Copy angle α (that’s a Greek “alpha”) to point A‘(that’s “A prime”)

Hint. You know how to copy a triangle, so make one to copy.

α

Euclid 9

Try this with some other angles if you need more practice..

A

●A'

Make an angle at A that’s twice as large as α.

Make an angle at B twice as large as β. (This is tricky…)

α

Euclid 10

β

A

B

Bisect (cut in half) angles α and β (Greek beta).

Hint. Create isosceles triangles and bisect their third sides…

α

Euclid 11

A

βB

Find the angle bisectors of each angle of this triangle.

What do you notice?

C

BA

Euclid 12

Try this with some other triangles.

Build a triangle with two angles α and β.

Then check that the third angle of that triangle is the same size as γ(gamma). Do you need a hint about how to do the check?

(Do this on another sheet of paper.)

α

Euclid 13

γβ

In this picture, angle α is a straight angle.

Bisect it. Now you’ve built a right angle!

Ask if you need a hint.

α

Euclid 14

●

Draw a line through point A that makes a right angle with line L.

Remember – no guessing.

Ask if you need a hint.

L

Euclid 15

●A

Draw a line through point A that is parallel to line L.

Hint. Draw any line through A and copy the angle that line makes where it meets L.

L

Euclid 16

●A