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

2. 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.

3. Make a copy of triangle ABC. C B A Euclid 3 Make up more triangles and copy them.

4. 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.

5. Make two or three different quadrilaterals with these four sides. Euclid 5 Make up more problems like this and solve them.

6. 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

7. 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.

8. Find the midpoints X, Y and Z of the sides of triangle ABC. Then draw AX, BY and CZ. What do you notice? C B A Euclid 8 Try this with some other triangles. X Y Z

9. 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'A'

10. 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

11. Bisect (cut in half) angles α and β (Greek beta). Hint. Create isosceles triangles and bisect their third sides… α Euclid 11 A β B

12. Find the angle bisectors of each angle of this triangle. What do you notice? C B A Euclid 12 Try this with some other triangles.

13. 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 γ β

14. 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 ●

15. 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

16. 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