MAFS.912.G-CO.4.12 Practice Lesson

MAFS.912.G-CO.4.12

Practice lesson

MAFS.912.G-CO.4.12

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

Constructing a perpendicular bisector

• You are given the Line Segment AB

• Step 1: Using your compass, draw an arc that is AT LEAST half the distance from A to B

Perpendicular Bisector cont...

• Step 2: Without changing the compass measurement, place the compass at point B and draw another arc

• Where your two arcs cross will create two more points. In the example those are Point X and Point Y

Perpendicular Bisector cont...

• Step 3: Draw a line through Point X and Point Y

• Where your new line, Line XY, crosses Line Segment AB is the midpoint, M.

• Perpendicular: where two lines cross and create 90 degree angles. Bisector: Splits what it crosses in half, sometimes creating a midpoint.

Fill in the Blank

What angle is created by a perpendicular?

_{You are given Angle A and Ray S. Construct an equivalent angle using a compass and Ray S}

• Step 1: Open the compass about two-thirds of the distance of one ray coming from Angle A.

• Step 2: Create and arc with the compass until It crosses the other ray of Angle A

Angle A cont...

• The new points created by the arc are Point B and Point C

• Step 3: Using the compass, measure the distance from Point A to Point B

• Step 4: Preserve the measurement and place the point of the compass on Point S and the pencil end on the ray.

Angle A cont...

• Where the pencil sits on the ray is going to be Point R

• Step 5: Create an arc from Point R

• (You may be asked what to find a congruent line segment. In this example, Line Segment AC is congruent to SR)

Angle A cont...

• Now that you have created the new arc coming from point R

• Step 6: Using the compass, measure the distance from Point B to Point C

• Step 7: Put the point of your compass at Point R and create another arc. Where the two arcs cross will be a new point, Point T

• Hint: (The arc from B to C is congruent to the arc from T to R)

Angle A cont...

• Step 8: Construct a ray from Point S through Point T

• The angle created is Angle S, and it is congruent to Angle A

• 
  

Multiple Choice

Suppose we wish to construct angle EFG congruent to angle DBC using a compass and straightedge. Which step would be correct to do first?

• Place the compass point at B

• Place the straightedge along A and C

• Place the compass point at C

• Place the straightedge along C and D

Constructing an angle bisector

• You are given Angle A

• Step 1: Create an arc by putting your compass at Point A and drawing the arc through both rays that come out of Point A

• The new points created are B and C

Angle Bisector cont...

• Step 2: Place your compass at point B and draw an arc

• Step 3: Place your compass at point C and draw an arc

• Where the two new arcs cross is Point D

Angle Bisector cont...

• Step 4: Draw a ray coming out of Point A and through Point D

• The new ray is the Angle Bisector

• The angle bisector splits the angle in half

Multiple Choice

Which of the following best describes the construction?

• Ray OC trisects angle BOA.

• Ray OC is parallel to ray OA.

• Ray OC is parallel to both rays OA and OB.

• Ray OC bisects angle BOA.

Copy the link to see a video about Transversals

https://tutors.com/math-tutors/geometry-help/proving-lines-are-parallel