Constructing a 60° Angle
Step 1: Draw a line segment using your your straightedge. Mark an endpoint and label label the endpoint P P .
P Step 2: Place the point of the compass at P . Create an arc, about a quarter of a circle in length, that intersects intersects the line segment. segment. Label this intersection intersection point as Q.
Q
P
Step 3: WITHOUT changing the length of the compass, place the point of the compass at Q. Draw an arc that intersects the first first arc. Label this new point of intersection as R.
R
Q
P
Step 4: Using your straightedge, straightedge, draw the ray ray PR. Angle RPQ is 60°. DO NOT ERASE ANY MARKINGS! The examiner want to see them!
R
P
Q
Constructing a 90° Angle
Step 1: Draw a line segment using your straightedge. Mark an endpoint and label the endpoint P .
P Step 2: Using your straightedge, extend the line past P such that there is “line space” on both sides of P :
P Step 3: Place the point of the compass at P . Draw two arcs: one should intersect the line to the left of P , and the other should intersect the line to the right of P . Label the two intersection points as Q and R.
Q
P
R
Step 4: OPEN THE COMPASS UP WIDER than before. Using Q as centre, draw an arc above P . Then, using R as centre, draw a second arc above P that intersects the first arc. Label this intersection point above P as S .
S
Q
P
R
Step 5: Using your straightedge, draw ray PS . Angle SPR is 90°. DO NOT ERASE ANY MARKINGS! The examiner wants to see them!
S
Q
P
R
Bisecting and Angle (helpful for forming angles of 30°, 45°, 150°, 135°, etc.)
Step 1: Draw an angle. Label its vertex as P .
P Step 2: Place the compass point at P, and draw an arc that intersects both rays of the angle. Label the two intersection points as Q and R.
R
P
Q
Step 3: Place the compass point at Q and draw an arc in the middle of the angle. Then place the compass point at R and draw a second arc that intersects the first arc. Label the intersection of the arcs as S .
R
P
S
Q
Step 4: Using your straightedge, draw ray PS . PS bisects angle RPQ. DO NOT ERASE ANY MARKINGS! The examiner wants to see them!
R
P
S
Q
Constructing a Parallel Line Through a Point Off the Line
Step 1: Draw a line segment. Mark two points on the line segment as P and Q. Draw a point above the line segment and label it R.
R
P
Q
Step 2: Open the compass to the length PQ. Using R as centre, draw an arc to the right of R.
R
P
Q
Step 3: Open the compass to the length PR. Using Q as centre, draw an arc that intersects the first arc. Label the intersection point S .
R
P
S
Q
Step 4: Using your straightedge, draw line RS . RS is parallel to PQ. DO NOT ERASE ANY MARKINGS! The examiner wants to see them!
R
P
S
Q
Constructing a Perpendicular Line Through a Point Off the Line (helpful for constructing altitudes)
Step 1: Draw a line segment. Mark two points on the line segment as P and Q. Draw a point above the line segment and label it R.
R
P
Q
Step 2: Using R as center, draw an arc that intersects PQ in two places. You may need to extend the line PQ is order to do this. Label the intersection points S and T .
R
S
P
Q
T
Step 3: Using S as centre, draw an arc below both R and the line segment. Then, using T as centre, draw another arc that intersects the previous arc. Label the intersection point U .
R
S
P
Q
T
U Step 4: Using your straightedge, draw RU . RU is perpendicular to PQ. DO NOT ERASE ANY MARKINGS! The examiner wants to see them!
R
S
P
T
U
Q
