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WorksheetsCoordinate Proofs
Total questions: 10
Worksheet time: 39mins
1. How is a coordinate proof different from other types of proofs you have studied?
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.
2. Explain why it is convenient to place a right triangle on the grid as shown when writing a coordinate proof.
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.
Select the graph that represents an isosceles right triangle with leg length p in the most convenient way.
Select the most convenient graph to represent a scalene triangle with one side length of 2m.
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.
Write a plan for the proof.
Given: G is the midpoint of HF
Prove: △GHJ≅△GFO
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.
Find the coordinates of the vertex O.
(a)
Find the coordinates of the vertex U.
(k, 0)
(0, k)
(k, 2k)
(2k, k)
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
