1.   Write a statement and reason for step 3.

Given: ABCD is a rectangle with diagonals
and
Prove:

   
   
    A. ; Opposite sides of a parallelogram are parallel
    B. is a right triangle; Definition of right triangle
    C. is a right angle; Definition of a rectangle
    D. ; Opposite sides of a parallelogram are congruent
    Hint

  2.   Complete step 4 of the proof.

Given: ABCD is a rectangle with diagonals
and
Prove:

   
   
    A. ; Opposite sides of a parallelogram are parallel
    B. ; Definition of midpoint
    C. and are right angles; Definition of a rectangle
    D. and are complimentary angles; Definition of complimentary angles
    Hint

  3.   What is the best statement for step 5?

Given: ABCD is a rectangle with diagonals
and
Prove:

   
   
    A. ; All right angles are congruent
    B. ; Opposite sides of a parallelogram are parallel
    C. ; Definition of midpoint
    D. is a right triangle; Definition of a right triangle
    Hint

  4.   Based upon steps 1-5, what is the best conclusion you can make for step 6? .

Given: ABCD is a rectangle with diagonals
and
Prove:

   
   
    A. ; SAS
    B. and are right triangles; Definition of a right triangle
    C. and are right triangles; Definition of a right triangle
    D. ; AAS
    Hint

  5.   If the seventh and final statement of the proof is , what reason can you give for making that statement?

Given: ABCD is a rectangle with diagonals
and
Prove:

   
    A. CPCTC
    B. SSS
    C. Hypotenuses of right triangles are congruent
    D. Definition of diagonals of parallelograms
    Hint



Glencoe
The McGraw-Hill Companies