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Euclid 1

Euclid 1. Find the point X where the lines joining A to B and C to D cross. Find the point Y where the lines joining A to C and B to D cross. C. B. ●. ●. A. ●. ●. D. Make up more problems like this and solve them. Euclid 2. Copy segment AB to line L starting at C. B. A. C. ●. L.

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Euclid 1

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  1. Euclid 1 Find the point X where the lines joining A to B and C to D cross. Find the point Y where the lines joining A to C and B to D cross. C B ● ● A ● ● D Make up more problems like this and solve them.

  2. Euclid 2 Copy segment AB to line L starting at C. B A C ● L Create segment DZ twice as long as AB starting at D on line M. D ● M Make up more problems like this and solve them.

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

  4. Euclid 4 Make a triangle with these three sides. Make a triangle with these three sides. Make up more problems like this and solve them.

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

  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. Euclid 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 Y X A B Z Try this with some other triangles.

  9. Euclid 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 A A' ● Try this with some other angles if you need more practice..

  10. Euclid 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…) β B α A

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

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

  13. Euclid 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.) β γ α

  14. Euclid 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

  15. Euclid 15 Draw a line through point A that makes a right angle with line L. Remember – no guessing. Ask if you need a hint. ● A L

  16. Euclid 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. A ● L

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