Coordinate Proofs

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)  

Tags

CCSS.5.G.A.1

Find the coordinates of the vertex U.

• (k, 0)

• (0, k)

• (k, 2k)

• (2k, k)

Tags

CCSS.6.G.A.3

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

Tags

CCSS.8.G.B.8

Which of these is a tool used in a coordinate proof?

• Midpoint formula

• screwdriver

• hammer

• level

Find the area of the quadrilateral on the coordinate plane

• 10 sq. units

• 6 sq. units 

• 8 sq. units

• 12 sq. units

Tags

CCSS.HSG.GPE.B.7

• 2
• 4
• -2
• 0

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

Find the distance.

• 7.1

• 7.8

• 8.7

• 8.9

Tags

CCSS.HSG.GPE.B.7

Find the distance between J and K.

• 8.2

• 7.7

• 9

• 10.2

Tags

CCSS.HSG.GPE.B.7

If you were graphing a polygon to create a coordinate proof where would the best place be to start?

• At the point (-2, 3) then graph the other corners where they land. 

• Start at the origin and put all the corners in the first quadrant. 

• It doesn't matter.

• Just copy the kid next to you, even if they have no idea what they are doing and they aren't even on the same question as you. 

Tags

CCSS.5.G.A.2