Name ______Date ______Period ______
Geometry – Triangle Proofs Ms. Hahl
Directions: Show all work on loose leaf. Where applicable, graphs are to be done on graph paper.
1) The coordinates of the vertices of are and Show that
is a scalene triangle.
2) The coordinates of the vertices of are and Show that
is a scalene triangle.
3) The coordinates of the vertices of are and Show that
is a scalene triangle.
4) If the vertices of are and show that is an isosceles
triangle.
5) The coordinates of the vertices of are and Using coordinate
geometry prove that is an isosceles triangle.
6) Show that is an isosceles triangle if its coordinates are and
7) If the vertices of are and show that it is an equilateral
triangle.
8) If the vertices of are and show that it is a right
triangle.
9) Show that is a right triangle if its coordinates are and
10) The coordinates of the vertices of are and Using
coordinate geometry prove that is an isosceles right triangle.
11) Show that is a right triangle if its coordinates are and
12) The coordinates of the vertices of are and Using
coordinate geometry prove that is an isosceles right triangle.
Recall the properties of your triangles:
1. Scalene - All 3 sides have different length
- Use distance formula 3x
2. Equilateral - All 3 sides have the same length
- Use distance formula 3x
3. Isosceles - Only 2 sides have the same length
- Use distance formula 3x
4. Right - 2 sides form a 90ο angle and the Pythagorean Theorem works!
2 options -
- Use slope formula 3x
- Use distance formula 3x and plug in to Pythagorean Theorem
1) The coordinates of the vertices of are and Show that
is a scalene triangle.
Need to complete the distance formula for and
is a scalene triangle because all three sides are different lengths.
5) The coordinates of the vertices of are and Using coordinate
geometry prove that is an isosceles triangle.
Need to complete the distance formula for and
is an isosceles triangle because two sides have the same length.
7) If the vertices of are and show that it is an equilateral
triangle.
Need to complete the distance formula for and
is an equilateral triangle because all three sides have the same length.
8) If the vertices of are and show that it is a right
triangle.
Need to complete the distance formula for and
Now we need to plug these lengths into the Pythagorean Theorem
is a right triangle because the Pythagorean Theorem is true and the Pythagorean
Theorem only works for right triangles.
8) If the vertices of are and show that it is a right
triangle.
Need to complete the slope formula for and
because they have negative reciprocal slopes and there is a right angle at
is a right triangle because the triangle contains a right angle.