SOLUTION: Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogramis a rhombus. State your plan and give a proof. Proof must include statements and re

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Question 174472: Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogramis a rhombus. State your plan and give a proof. Proof must include statements and reasons.
Given: ABCD is a parallelogram with <1 = (w/ wavy line above it) <2.
To Prove: ABCD is a rhombus.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogramis a rhombus. State your plan and give a proof. Proof must include statements and reasons.
Given: ABCD is a parallelogram with Ð1 @ Ð2.
To Prove: ABCD is a rhombus.

 

 1. ABCD is a parallelogram           1. Given
 2. AB || CD                           2. Opposite sides of a
                                         parallelogram are parallel
 3. Ð1 = Ð2                          3. Given

 4. Ð1 = Ð3                          4. Alternate interior angles
                                         formed when transversal AC
                                         cuts parallel lines AB and
                                         CD.
 5. Ð2 = Ð3                          5. Things equat to the same 
                                                 thing are equal to each 
                                                 other
                                        
 6. Ð2 @ Ð3                          6. Angles congruent to the
                                         same angle are congruent.
 7. DACD is isosceles                 7. Base angles 2 and 3 are
                                         congruent
 8. AD @ CD                           8. Legs of an isosceles
                                         triangle are congruent
 9. AD @ BC                         9. Opposite sides of a
                                         parallelogram are congruent 
10. CD @ AB                          10. Opposite sides of a
                                         parallelogram are congruent
11. AB @ BC @ CD @ AD                11. By 8,9, and 10 and "things
                                         congruent to the same thing
                                         are congruent to each other".
12. ABCD is a rhombus                12. All 4 sides are congruent. 

Edwin