You do not need to write a plan for a coordinate proof.

You do not have a Given or Prove statement.

You have to assign coordinates to vertices and write expressions for the side lengths and slopes of segments.

You can only do coordinate proofs with triangles.

The hypotenuse of the right triangle is easy to identify.

The side lengths are often easier to find because you are using zeros in your expressions.

It is easier to dilate the figure on the coordinate plane.

Both legs have the same length when you place the triangle on the x- and y-axes.

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 G using the Midpoint Formula
Use these coordinates and the Distance formula to show that OG ≅ JG.
Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.

Find the coordinates of G using the Distance Formula
Use these coordinates and the Midpoint formula to show that OG ≅ JG.
Show that HG≅ FG by the definition of midpoint and ∠HGJ ≅ ∠FGO by the Vertical Angles Congruence Theorem.

Then, use the SAS Congruence Theorem to conclude that △GHJ ≅ △GFO.

Then, use the SSS Congruence Theorem to conclude that △GHJ ≅ △GFO.

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