MJJ Geometry - Explore and Apply Ancient Greece Constructions
First Student Challenge: Can you copy a line segment?
• Step 1: Construct a circle using circle with center through point tool.[br]• Step 2: Mark the circle’s center and label it point [math]A[/math].[br]• Step 3: Mark a point on the circle and label it point [math]B[/math].[br]• Step 4: Draw [math]AB[/math][br]• Step 5: Draw point [math]C[/math] somewhere outside of your circle.
Follow directions above to complete construction of line segment and then Using only an line segment tool and compass, can you construct another line segment the same length of AB beginning at point C?
Write instructions that explain the steps you used to complete the construction of your new segment containing C that is the same length as original segment AB.
Second Student Challenge: Can you copy an angle?
Now that you know how to copy a segment, copying an angle is easy.[br][br]First create an angle.[br]Step 1: Create an angle of any size and label it [math]∠ABC[/math] using the angle tool, Select the angle tool then click 3 points in a clockwise order on the plane and let [math]B[/math] be the vertex of that angle. [br][br]Step 2: Using the line segment tool Connect the point [math]A[/math] to [math]B[/math] and [math]B[/math] to [math]C[/math]. The angle is at vertex [math]B[/math][br][br]Step 3: Construct a point away from [math]∠ABC[/math] and label it point [math]E[/math][br] [br] [br]
Using your tools, create a copy of ∠ABC with point E and label it ∠DEF.
How would you construct a copy of an angle at a new point? Justify why your construction works. Be prepared to share your ideas with the class.
APPLY Third Student Challenge: The Proof is in the Distance
Step 1: Create a line segment and label it [math]AB[/math][br]Step 2: Create a perpendicular bisector for the line segment and label it [math]CD[/math][br]Step 3: Create two additional points collinear with [math]CD[/math]and label them point [math]E[/math] and point [math]F[/math] respectively.[br]
Prove point E and point F are equidistant from point A and Point B.
Be prepared to share your ideas with the class
Fourth Student Challenge: The Great Angle Bisector
Goal: Determine the angle bisector[br][br]First create an angle [br]Step 1:Create an angle using the angle tool and let [math]B[/math] be the vertex of that angle. [br][br]Step 2: Once you select the angle tool then click 3 points in a clockwise order on the plane.[br]Step 3: Using the line segment tool Connect the point [math]A[/math] to [math]B[/math] and [math]B[/math] to [math]C[/math]. The angle is at vertex [math]B[/math][br][br][br]
Determine a way to bisect the angle
Be prepared to share your ideas with the class
REFLECT
Which construction do you find the easiest? Why?
REFLECT
Which construction do you find the hardest? Why?