Developing Proof Complete the Following Coordinate Proofs

Name

Class

Date

Proofs Using Coordinate Geometry

6-9

Practice

Form K

Developing Proof Complete the following coordinate proofs.

1. TriangleMidsegmentTheorem

Given: ABC

D is the midpoint of .

Eisthemidpointof. Prove:.

a. FindthecoordinatesofDandE.

To start, use the Midpoint Formula.

or D( , )

or E( , )

b. FindDEandCB.

To start, use the Distance Formula. =

c. Findtheslopeofandtheslopeof.Explain.

2. Reasoning In Exercise 1, explain why it is easier to use the coordinates (0, 2h), (2a, 0), and (2a, 0), rather than (0, h), (a, 0), and (a, 0).

3. Aparallelogramisasquare.

Given:GHIJ

Prove: GHIJ is a square.

a.FindGIandHJ.

b.FindtheslopesofGIandHJ.

Prentice Hall Foundations Geometry • Teaching Resources

Name

Class

Date

Proofs Using Coordinate Geometry

6-9

Practice (continued)

Form K

Tell whether you can reach each type of conclusion below using coordinate methods. Give a reason for each answer.

4. mA = mG5. ∆ABC∆GHI

6. QuadrilateralABCDisarectangle.7. ∆HIJisequiangular.

8. Thebaseanglesofanisoscelestrapezoidarecongruent.

9. QuadrilateralWXYZisaparallelogram.

10. Think About a Plan If the diagonals of a quadrilateral are perpendicular but do not bisect each other, then the quadrilateral is a kite.

•How will you place the quadrilateral in the coordinate plane?

•What formula(s) will you use?

•What are the coordinates of the vertices?

Use coordinate geometry to prove each statement.
11. Thevertexofanisoscelestriangleisontheperpendicular
bisector of the base.

12. ∆ABCisaright,isoscelestriangle.

Prentice Hall Foundations Geometry • Teaching Resources