1. The document provides instructions for constructing different types of triangles given specific properties: equilateral triangles given one side, isosceles triangles given two sides, scalene triangles given three sides, and right triangles given the hypotenuse and one leg. 2. The steps involve using a compass to draw arcs with the given side lengths and finding the point of intersection to determine the third vertex. 3. Lines are then drawn between the vertices to complete the triangle.

1. CONSTRUCTING TRIANGLES

2. Exercise 1
Construct an equilateral triangle given one side

3. We have one side of the
triangle. We know that
the equilateral triangle
has three equal sides

4. STEPS:
1.Center your compass at
point A and open it to point
B. Draw an arc

5. STEPS:
1.Center your compass at
point A and open it to point
B. Draw an arc

6. STEPS:
2.Now, center your compass
at point B and open it to
point A. Draw an arc

7. STEPS:
2.Now, center your compass
at point B and open it to
point A. Draw an arc

8. STEPS:
3.The intersection of both
arcs is the point C that is
the third vertex of the
triangle

9. STEPS:
4.Join point A with C

10. STEPS:
4.Now join point C with B
and you obtain the
equilateral triangle

11. Exercise 2
Construct an isosceles triangle given two sides

12. We know that the isosceles
triangle has two equal
sides. We have one of the
side that is equal to the
other (a=b) and the side
that is different (c)

13. STEPS:
1.Take the length of the side
that is equal to the other
(a=b)

14. STEPS:
2.Draw with this length an
arc centering at A

15. STEPS:
3.With the same length draw
another arc centering at B

16. STEPS:
4.The point C is where both
arcs intersect. The point C
is the third vertex of the
triangle
C

17. STEPS:
5.Join point A with C
C

18. C
STEPS:
5.Now join point C with B
and you obtain the
isosceles triangle

19. Exercise 3
Construct a scalene triangle given its three sides

20. We know that the scalene
triangle has its three sides
different. We have one of
its sides, the side c

21. STEPS:
1.Take the length of the side
b and transport it centering
on the left endpoint of the
side c

22. STEPS:
1.Take the length of the side
b and transport it centering
on the left endpoint of the
side c

23. STEPS:
2.Take the length of the side
a and transport it centering
on the right endpoint of the
side c

24. STEPS:
3.The third vertex of the
triangle is where both arcs
intersect

25. STEPS:
4.Join this vertex with the
other vertices and you
obtain the scalene triangle

26. STEPS:
4.Join this vertex with the
other vertices and you
obtain the scalene triangle

27. Exercise 4
Construct a right triangle given the hypotenuse and one leg

28. We know that the rectangle
triangle has a right angle.
We have one leg of the
triangle ( c ) and the
hypotenuse ( a )

29. STEPS:
1.Draw a perpendicular line
that passes through the left
endpoint of the side c. Uses
the method you know

30. STEPS:
1.Draw a perpendicular line
that passes through the left
endpoint of the side c. Uses
the method you know

31. STEPS:
1.Draw a perpendicular line
that passes through the left
endpoint of the side c. Uses
the method you know

32. STEPS:
1.Draw a perpendicular line
that passes through the left
endpoint of the side c. Uses
the method you know

33. STEPS:
1.Draw a perpendicular line
that passes through the left
endpoint of the side c. Uses
the method you know

34. STEPS:
1.Draw a perpendicular line
that passes through the left
endpoint of the side c. Uses
the method you know

35. STEPS:
2.Take the length of the
hypotenuse and transport
it centering on the right
endpoint of the segment

36. STEPS:
2.Take the length of the
hypotenuse and transport
it centering on the right
endpoint of the segment

37. STEPS:
3. The third vertex of the
triangle is where the arc
intersects the perpendicular
line. Join this vertex with the
right endpoint of the side c
and you obtain the right
triangle