Triangles (3.3.2)

Question 1

• Collinear: any two or more points that fall on the same line.

Answer 1

• Collinear: any two or more points that fall on the same line.

Question 2

• Three points are collinear any time that the sum of any two lengths between two points is equal to the third length between
two points.

Answer 2

• Three points are collinear any time that the sum of any two lengths between two points is equal to the third length between
two points.

Question 3

• Three points form a triangle any time that the sum of any two lengths between points is longer than the third length between
two points.

Answer 3

• Three points form a triangle any time that the sum of any two lengths between points is longer than the third length between
two points.

Question 4

• Three points form a right triangle any time any two lengths squared add up to the third length squared.

Answer 4

• Three points form a right triangle any time any two lengths squared add up to the third length squared.

Question 5

Calculate the three lengths between each pair of points.
Here are the calculations for (A, B).
Here are the calculations for (A, C) and (B, C).
These points are not collinear because no two sums add up
to the third one.
The three points meet the test for being a right triangle: two
of their lengths squared do add up to the third length squared.

Answer 5

Calculate the three lengths between each pair of points.
Here are the calculations for (A, B).
Here are the calculations for (A, C) and (B, C).
These points are not collinear because no two sums add up
to the third one.
The three points meet the test for being a right triangle: two
of their lengths squared do add up to the third length squared.