Coordinate Plane Proofs

Write a plan for the proof. Given Coordinates of vertices of △OPM and △ONM Prove △OPM and △ONM are isosceles triangles

• Find the lengths of OP, PM, MN, NO and OM to show that △OMP≅△OMN by the SSS Congruence Theorem.

• Find the lengths of OP, PM, MN, and NO to show that OP ≅ PM and MN ≅ NO.

Find the coordinates of the vertex O.

You and your cousin are camping in the woods. You hike to a point that is 500 meters east and 1200 meters north of the campsite. Your cousin hikes to a point that is 1000 meters east of the campsite.

The distance from the campsite to you is ______ meters.

• 1500

• 1300

• 1200

• 1000

You and your cousin are camping in the woods. You hike to a point that is 500 meters east and 1200 meters north of the campsite. Your cousin hikes to a point that is 1000 meters east of the campsite.

The distance from you to your cousin is ______ meters.

• 1500

• 1300

• 1200

• 1000

Find the coordinates of the vertex U.

• (k, 0)

• (0, k)

• (k, 2k)

• (2k, k)

To prove two sides are parallel we use the

• distance formula

• slope formula

• midpoint formula

To prove two sides are perpendicular we use the _____________ and look for negative reciprocals

• distance formula

• slope formula

• midpoint formula

To prove two sides are congruent we use the

• distance formula

• slope formula

• midpoint formula

What must be true if two segments are parallel to each other?

• They have equal slopes

• They have negative reciprocal slopes

• Their lengths are equal

• Their lengths are whole numbers

What must be true if two segments are perpendicular to each other?

• They have equal slopes

• They have negative reciprocal slopes

• Their lengths are equal

• Their lengths are whole numbers