Name_________________________
NOTES
Coordinate Geometry Proofs
Secondary Math 2
Important formulas (YOU NEED TO KNOW THESE!)
Slope:
Midpoint:
Distance (length):
THREE PARTS
Prove triangles are:
-right
-scalene
-isosceles
-equilateral
-congruent using SSS or SAS
1. Formulate a plan
2. Use slope, midpoint, and/or distance
formulas to execute plan
3. Create concluding statement to
justify the proof
Methods of Proof
Right Triangle
-using the slope formula, prove that two sides are perpendicular (right angle)
Scalene Triangle
-using the distance formula, prove that none of the sides are congruent
Isosceles Triangle
-using the distance formula, prove that only two sides are congruent
Equilateral Triangle
-using the distance formula, prove that all sides are congruent
1) Triangle AFN has vertices A(-7, 6), F(-1, 6), and N(-4, 2). Prove triangle AFN is an isosceles
triangle.
2) Triangle MEP has vertices M(6, 12), E(6, 4), and P(3, 8). Prove triangle MEP is an isosceles
triangle but not right.
3) The vertices of triangle ABC are A(0, 0), B(2, 3), and C(4, 0). Using coordinate geometry,
write a proof to classify the triangle.
4) Triangle WXY with vertices W(3, -7), X(6, -7), Y(6, -2) is a transformation of triangle RST
with vertices R(2, 0), S(5, 0), and T(5, 5). Graph the original figure and its image. Identify the
transformation and verify that it is a congruence transformation.
Name_________________________
Secondary Math 2
Date_________
Coordinate Geometry Proofs
1) Prove that A(1, 1), B(4, 4), and C(6, 2) are the vertices of a right triangle.
2) The vertices of ABC are A(-3,1), B(-2,-1), and C(2,1). Prove that ABC is a right triangle.
3) The vertices of ABC are A(-1,5), B(5,3) and C(1,1). Prove that ABC is an isosceles right
triangle.
4) Triangle TRI has vertices T(-5,5), R(5,1), and I(5,9). Using coordinate geometry, write a
proof to classify triangle TRI.
5) Triangle DAN has coordinates D(-10,4), A(-4,1), and N(-2,5) Using coordinate geometry,
write a proof to classify triangle DAN.
6) The vertices of triangle JEN are J(2,10), E(6,4), and N(10,8). Using coordinate geometry,
write a coordinate proof to classify triangle JEN.
7) The coordinates of the vertices of triangle SUE are S(-2,-4), Y(2,-1), and E(8,-9). Using
coordinate geometry, prove that:
a) triangle SUE is a right triangle;
b) triangle SUE is not an isosceles right triangle.
8) Triangle ART has vertices A(a,b), R(a + c,b), and T(a + c/2, b + d). Using coordinate
geometry prove that triangle ART is isosceles.
9) The vertices of
?
1)
2)
3)
4)
are
and
Which conclusion can be made about the angles of
10) Triangle ABC has coordinates
,
, and
. Find the perimeter of the triangle.
Express your answer in simplest radical form. [The use of the grid below is optional.]
11) . The vertices of triangle JKL are J(−3, 0), K(−2, 4), L(−1, 0), and the vertices of triangle
QRS are Q(2, −4), R(3, 0), S(4, −4). Use coordinate geometry to prove the triangles congruent.
12) The vertices of triangle ABC are A(1, 3), B(1, 1), C(4, 1), and the vertices of triangle DEF
are D(3, -1), E(1, -1), F(1, -4). Use coordinate geometry to prove the triangles congruent.