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
is a scalene triangle.
are
and
Show that
2) The coordinates of the vertices of
is a scalene triangle.
are
and
Show that
3) The coordinates of the vertices of
is a scalene triangle.
are
4) If the vertices of
triangle.
are
and
5) The coordinates of the vertices of
are
geometry prove that
is an isosceles triangle.
6) Show that
are
8) If the vertices of
triangle.
are
show that
is an isosceles
and
Using coordinate
and
and
show that it is an equilateral
and
show that it is a right
is a right triangle if its coordinates are
10) The coordinates of the vertices of
coordinate geometry prove that
11) Show that
Show that
is an isosceles triangle if its coordinates are
7) If the vertices of
triangle.
9) Show that
and
are
and
is an isosceles right triangle.
is a right triangle if its coordinates are
12) The coordinates of the vertices of
coordinate geometry prove that
are
and
is an isosceles right triangle.
and
Using
and
Using
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
is a scalene triangle.
are
and
Need to complete the distance formula for
Show that
and
is a scalene triangle because all three sides are different lengths.
5) The coordinates of the vertices of
are
geometry prove that
is an isosceles triangle.
Need to complete the distance formula for
and
Using coordinate
and
is an isosceles triangle because two sides have the same length.
7) If the vertices of
triangle.
are
and
Need to complete the distance formula for
show that it is an equilateral
and
is an equilateral triangle because all three sides have the same length.
8) If the vertices of
triangle.
are
Need to complete the distance formula for
and
show that it is a right
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
triangle.
are
Need to complete the slope formula for
and
show that it is a right
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.