using vertex theorem

Find the coordinates of the vertex O.

Select all that are TRUE.

• AB > AE

• BE > CE

• BE > CD

• CD < DE

• CE > BC

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.

What is the chromatic number of this graph?

• 2

• 3

• 4

• 5

A point that divides, or bisects, a segment into two congruent segments is called a ___________________.

• midpoint
• congruent segment
• angle bisector
• endpoint

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

Five scout leaders are taking their troops to an overnight scout competition in NYC. Because of limited funds, there are only 3 rooms that are free for the 5 scout leaders to stay in. Some scout leaders have differences of opinions as to how they lead their troops and cannot share a room, as shown here. Is there a way that these 5 scout leaders can spend the night at the hotel using these 3 free rooms?

• YES, they can use 3 rooms.

• NO, they need 4 rooms.

• No, they need 5 rooms.

• No, they only need 2 rooms

What color should Vertex 4 be?

• red

• yellow

• purple

• blue

Name the angles from SMALLEST to LARGEST

• Q, R, P
• P, Q, R
• R, P, Q
• R, Q, P

The Four Color Theorem's proof was significant because:

• it showed that the world i round

• it costs a lot of money

• it was the first proof that was computer aided

• it took so long to write