Triangles in Coordinate Planes & Proofs

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  • 0:04 Triangles in a Plane
  • 1:55 SAS Proof
  • 2:25 Example Problem
  • 4:13 Lesson Summary
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Lesson Transcript
Instructor: Contractor Resources
When you draw a triangle in a coordinate plane, you can use the coordinates on the plane to find information about the triangle. You can even do proofs with triangles in a plane. Watch this lesson to learn how.

Triangles in a Plane

You've probably seen triangle problems that look like this, and if you can do that triangle, you can do the exact same thing in a coordinate plane. A coordinate plane, also called a Cartesian plane, is a graphical system that plots points on two axes, a horizontal x-axis and a vertical y-axis.

Each point on the coordinate plane is represented by two numbers: an x coordinate and a y coordinate. The x coordinate tells whether the point is left or right of the middle of the graph, and how far. Positive x values represent points further to the right, and negative x values represent points further to the left. The y coordinate tells whether the point is above or below the middle of the graph, and how far. Positive y coordinates represent points further up, and negative y coordinates represent points further down. To show any point on the coordinate plane, just write (x, y). For example, the point (5, 3) is 5 units to the right of center, and 3 units above center.

When you're working with a triangle in a coordinate plane, just use the coordinate plane to help you find the dimensions of the triangle. For example, you can see that these two triangles are actually the same triangle. In the coordinate plane, the bottom of the triangle stretches along the x-axis from -4 to 5, so it's 9 units long. The left side of the triangle stretches along the y-axis from -7 to 5, so it's 12 units long. You can work with the triangle in the coordinate plane just like you'd work with any other triangle; just use the coordinates to find the dimensions of the triangle and work from there.

SAS Proof with Triangles in a Plane

You can even do proofs with triangles in a coordinate plane, just like you can with any other triangles. For an example, let's do a proof that two triangles are congruent using the side-angle-side theorem. The side-angle-side theorem, abbreviated SAS, states that if two triangles have two equal sides, and if the interior angle is the same in both triangles, then the triangles are congruent. The interior angle is the angle between the two pairs of congruent sides.

Example Problem

Now, let's use that theorem to prove the congruence of two triangles in a coordinate plane.

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