document.write( "Question 1010765: Hello. I was wondering if I could get some assistance on this proof for my geometry class. I have been trying to find out the best way to do the problem, but this is new ground for me. \r
\n" ); document.write( "\n" ); document.write( "Given: The diagonals of parallelogram PARL are congruent.
\n" ); document.write( "Prove: PARL is a rectangle. \r
\n" ); document.write( "\n" ); document.write( "Your help is much appreciated.
\n" ); document.write( "Thanks so much in advance. \n" ); document.write( "

Algebra.Com's Answer #626229 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let's draw out the picture. Let's assume PARL is a rectangle. This drawing (below) does NOT prove it is a rectangle. The table after the drawing is what will prove the claim. The drawing is simply a tool to help visualize the proof.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Proof Table\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

Number	Statement	Reason
1	PARL is a parallelogram	Given
2	The diagonals of PARL are congruent	Given
3	PR = AL	Diagonals are congruent
4	PA = RL	Opposite sides of a parallelogram are congruent
5	AR = LP	Opposite sides of a parallelogram are congruent
6	Triangle APL = Triangle RLP	SSS Property of Congruence
7	Angle APL = Angle RLP	CPCTC
8	Triangle PAR = Triangle LRA	SSS Property of Congruence
9	Angle PAR = Angle LRA	CPCTC
10	(Angle APL)+(Angle RLP) = 180	Same Side Interior angles are supplementary
11	(Angle APL)+(Angle APL) = 180	Substitution (lines 10 and 7)
12	2*(Angle APL) = 180	Combine like terms
13	Angle APL = 90 degrees	Division Property of Equality
14	90 degrees = Angle RLP	Substitution (lines 7 and 13)
15	Angle RLP = 90 degrees	Symmetric Property of Equality
16	Angle ARL = Angle APL	Opposite angles of a parallelogram are congruent
17	Angle ARL = 90 degrees	Substitution (lines 16 and 13)
18	Angle PAR = Angle RLP	Opposite angles of a parallelogram are congruent
19	Angle PAR = 90 degrees	Substitution (lines 18 and 15)
20	PARL has 4 right angles	See lines 13,15,17,19
21	PARL is a rectangle	Definition of Rectangle (see note)

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: A rectangle is simply a quadrilateral with 4 right angles (aka 90 degree angles). \n" ); document.write( "

\n" );