Download ∆1: Additional Thoughts: Classify the ∆ by its angles: Where do the 3

Name: ________________________
Date: ____________
Geometry
Section 5.1
A perpendicular bisector of a triangle is a segment that is perpendicular
to another segment at its midpoint.
1. Follow the steps below to create 3 perpendicular bisectors on each triangle.
Step 1) Place the compass point on point D. Use a compass setting more than half the length of DE.
Draw two large arcs; one on the left side of 𝐷𝐸, the other below 𝐷𝐹.
Step 2) Use the same setting, with compass point on point E, to draw two arcs that intersect the arcs
you made in step 1.
Step 3) Using one of your colors and a straightedge, connect the arcs’ point
of intersection. This segment is the perpendicular bisector of 𝐷𝐸.
Step 4) Repeat steps 1 – 3 to create the perpendicular bisectors for 𝐸𝐹 and 𝐷𝐹.
(For 𝐸𝐹, place the compass on point E and use a compass setting more than half of 𝐸𝐹 to create the first two arcs. Place the
compass point on F to get the second set of arcs. Use a different color to connect the points of intersection.)
(For 𝐷𝐹, place the compass on point F and use a compass setting more than half of 𝐷𝐹 to create the first two arcs. Place the
compass point on D to get the second set of arcs. Use a different color to connect the points of intersection.)
∆1:
Additional Thoughts:
E
Classify the ∆ by its angles: _________________
D
F
∆2:
Where do the 3 perpendicular bisectors intersect?
(circle one): inside the ∆, outside the ∆, on the ∆
Additional Thoughts:
E
Classify the ∆ by its angles: _________________
D
Where do the 3 perpendicular bisectors intersect?
(circle one): inside the ∆, outside the ∆, on the ∆
F
∆3:
Additional Thoughts:
E
D
Classify the ∆ by its angles: _________________
F
Where do the 3 perpendicular bisectors intersect?
(circle one): inside the ∆, outside the ∆, on the ∆
An angle bisector of a triangle is a segment from a vertex of the triangle to the
opposite side, dividing the vertex angle into two congruent angles.
2. Follow the steps below to create 3 angle bisectors on each triangle.
Step 1) Place the compass point on point D. Draw a large arc that intersects the sides of angle D (𝐷𝐸
and 𝐷𝐹). Label the points of intersection A and B.
Step 2) Use the same setting, with compass point on point A, to draw an arc away from ∠D (to the right).
Step 3) Use the same setting, with compass point on point B, to draw an arc away from ∠D, that
intersects the arc you made in step 2. Label the point of intersection X.
Step 4) Using one of your colors and a straightedge, draw a segment connecting point D and point X.
Step 5) Repeat steps 1 – 4 to create the angle bisectors of ∠E and ∠F.
Use a different color each time you connect step 4.
∆4:
Additional Thoughts:
E
Classify the ∆ by its angles: _________________
D
F
∆5:
Where do the 3 perpendicular bisectors intersect?
(circle one): inside the ∆, outside the ∆, on the ∆
Additional Thoughts:
E
Classify the ∆ by its angles: _________________
D
Where do the 3 perpendicular bisectors intersect?
(circle one): inside the ∆, outside the ∆, on the ∆
F
∆6:
Additional Thoughts:
E
D
Classify the ∆ by its angles: _________________
F
Where do the 3 perpendicular bisectors intersect?
(circle one): inside the ∆, outside the ∆, on the ∆