euclidean constructions

Question 1

Bisecting a segment

Answer 1

dividing a line into equal halves

Question 2

isosceles triangle

Answer 2

a triangle with two equal sides

Question 3

equilateral triangle

Answer 3

a triangle with three equal sides

Question 4

constructing a 60 degree angle and its 30 degree bisector

Answer 4

1. create an equilateral triangle
   - the total sum of a triangle is 180 degrees
   - an equilateral triangle is equal on all sides
   - 180 degrees divided by three angles/points of triangle results in three 60 degree angles
2. create a perpendicular bisector on one line of triangle
   - results in one 60 degree angle being divided in half, creating two 30 degree angles

Question 5

perpendicular through a given point to a given line

Answer 5

1. using the point as the center, create a circle that over laps with part of the line
2. create a perpendicular bisector on the line that’s in the circle

Question 6

square on a given AB segment

Answer 6

1. perpendicular bisector through A
   - extend the segment
   - create helper points around A
   - using the helper points, create a bisector
2. find the third point (D) of the square
   - using A as the center, create a circle that extends to B
   - D is wherever the circle connects on the bisector line
3. find the fourth point (C)
   - using the same length (from A to B), create a circle with D as the center
   - create another circle with B as the center
   - C is where the two circles connect

Question 7

duplicate an angle on a given segment

Answer 7

1. find a length of the angle
   - using the smallest part of the angle (O) as the center, create a circle that results in two arbitrary lines (points B and C) being placed towards the opening of the crescendo
   - use this same measurement on the given segment, using a point as the center (replicating O), and create a circle around the segment (point D, replicating B)
2. find the distance between the angle
   - measure the distance between B and C, then create a circle around D
   - point E (replicating C) is where the two circles on the segment intersect
3. connect A to E, the angle has been duplicated

Question 8

parallel line through a point

Answer 8

1. create a random line (a transversal) that goes through A and the given line
   - mark the intersection of the transversal and the given line (X)
2. using X as the center point, create an arc through the transversal and the given line (D and C)
   - using A as the center, create the same arc through the transversal (F)
3. using the radius of CD, create a circle around F
   - the intersection of the circle with the arc is E
4. draw a line through A and E

Question 9

center of a circle from three points (A, B, C)

Answer 9

1. connect points A and B
   - using the same radius, create full circles around points A and B (perpendicular bisector)
2. connect points B and C
   - create another perpendicular bisector on this segment
   - the intersection of these bisectors is point O
3. using O as the center, create a circle that goes through ABC

Question 10

tangent (touching) circles with a given center A

Answer 10

1.

Question 11

divide a segment into equal parts

Question 12

geometric multiplication