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Can you construct your own algebraic proof?

In the previous example, you used the distance formula and four points in a coordinate plane to construct an algebraic proof. Now, construct your own algebraic proof.

four points in a coordinate plane

Prove or disprove that figure EFGH is a rectangle. Construct your proof by answering the multiple choice questions that follow.

1. In order to prove that EFGH is a rectangle, you need to know rectangle properties.  Which of the following is NOT a property of rectangles?

  1. Opposite sides are congruent.
  2. Opposite sides are parallel.
  3. All vertices are right angles.
  4. All vertices are acute angles.

Acute angles are less than 90°.  Are the vertices of a rectangle less than 90° or equal to 90°?

Acute angles are less than 90°.  Are the vertices of a rectangle less than 90° or equal to 90°?

Acute angles are less than 90°.  Are the vertices of a rectangle less than 90° or equal to 90°?

Acute angles are less than 90°.  Are the vertices of a rectangle less than 90° or equal to 90°?

2. Next, you need to define the points at each vertex.  Which of the following points is NOT a point at the vertex of EFGH?

  1. (-6, 12)
  2. (-6, 9)
  3. (-6, 6)
  4. (-13, 12)
  5. (-13, 9)

Label the (x,y) coordinates for points E, F, G, and H.

Label the (x,y) coordinates for points E, F, G, and H.

Label the (x,y) coordinates for points E, F, G, and H.

Label the (x,y) coordinates for points E, F, G, and H.

Label the (x,y) coordinates for points E, F, G, and H.

3. What is the length of FG?

  1. 7
  2. 3
  3. 10
  4. 4

Count the number of units between F and G.

Count the number of units between F and G.

Count the number of units between F and G.

Count the number of units between F and G.

4. What is the length of EH?

  1. 7
  2. 3
  3. 10
  4. 4

Count the number of units between E and H.

Count the number of units between E and H.

Count the number of units between E and H.

Count the number of units between E and H.

5. What is the length of EF?

  1. 7
  2. 3
  3. 10
  4. 4

Count the number of units between E and F.

Count the number of units between E and F.

Count the number of units between E and F.

Count the number of units between E and F.

6. What is the length of GH?

  1. 7
  2. 3
  3. 10
  4. 4

Count the number of units between G and H.

Count the number of units between G and H.

Count the number of units between G and H.

Count the number of units between G and H.

7. Based on your calculations, is EFGH a rectangle?

  1. Yes
  2. No

Does EFGH have four right angles with opposite sides that are congruent and parallel?

Does EFGH have four right angles with opposite sides that are congruent and parallel?

Summary

Questions answered correctly:

Questions answered incorrectly: