Download Triangle Side Lengths and Angle Measures

Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
Triangle Side Lengths and Angle Measure
Key Words:
Triangle, angle measure, opposite sides
Summary:
Students will construct a triangle and investigate the relationship between the measure of
the angles of the triangle and the length of the sides opposite those angles
Existing Knowledge:
It is assumed that the students will have been exposed to and are familiar with locating an
angle of a triangle and finding its opposite side. They also need to know the following
definitions as they relate to triangles: acute, obtuse, right, scalene, and isosceles.
NCTM Strand:
Analyze characteristics and properties of two-dimensional and three-dimensional
geometric shapes and develop mathematical arguments about geometric relationships.
State Strand:
Geometry and Spatial Sense (Prove theorems involving properties of lines, angles,
triangles, and quadrilaterals)
Learning Objectives:
1. Construct a triangle
2. Measure all sides and interior angles of the triangle
3. Investigate the relationship between the measure of the angles of the triangle and
the length of the sides opposite those angles
Materials:
Computer lab or set of calculators equipped with Cabri Geometry II and the lab
worksheet
Procedures:
*Have students work in pairs to perform the following construction
*Students will be assessed by turning in their lab sheets along with a copy of the
construction made
Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
Triangle Side Lengths and Angle Measure
Team Members:
File Name:
_____________________
_____________________
_____________________
Goal 1: Construct a triangle and measure all angles and the sides opposite those
angles.
Investigate using Cabri Geometry II
1. Construct V ABC
(triangle tool)
2. Measure and label ∠ABC , ∠ BCA ,
and ∠CAB
(angle tool)
3. Measure and label sides AB , BC , and AC
(distance/length tool)
4. Drag the measure of ∠ABC to an unoccupied space on the screen, and then drag
the measure for its opposite side ( AC ) next to the angle measurement (repeat this
process for the other 2 angles and their corresponding opposite sides)
What do you notice about the relationship between the measure of each angles
and the length of its opposite side?
_______________________________________________
*In a triangle, the length of the side opposite the angle with the largest degree measure
will be the longest side. Likewise, the length of the side opposite the angle with the
smallest degree measure will be the shortest side.
Goal 2: Investigate if the statement above appears to be true for obtuse, acute, and
right triangles.
1.
Drag one of the vertices of the triangle so that it is an obtuse triangle. Does
your conjecture above hold
true?__________________________________________
2. Drag one of the vertices of the triangle so that it is an acute triangle. Does
your conjecture above hold true?
_______________________________________________
3. Drag one of the vertices of the triangle so that it is a right triangle. Does your
conjecture above hold true?
_______________________________________________
Project AMP
Dr. Antonio R. Quesada – Director, Project AMP
Goal 3: Investigate if the statement above appears to be true for isosceles triangles
1. Draw a circle, label the center X
(circle tool)
2. Draw any two radii and label their endpoints on the circle Y and Z.
(segment tool)
3. Draw YZ
(segment tool)
4. Hide the circle
(hide/show tool)
5. Measure ∠XYZ , ∠ YZX , and ∠YXZ
(angle tool)
6. Measure XY , XZ , and YZ
(distance/length tool)
7. Drag the measure of ∠XYZ to an unoccupied space on the screen, and then
drag the measure for its opposite side ( XZ ) next to the angle measurement
(repeat this process for the other 2 angles and their corresponding opposite
sides)
8. What conjecture can you make about the angles and opposite sides of an
isosceles triangle?
_________________________________________________________
_________________________________________________________
9. Drag one of the vertices of the triangle. Does
your conjecture about isosceles triangles hold
true?___________________________________
10. Repeat the process for the other vertices. Does your
conjecture about isosceles triangles hold true?
_____________________________________