1. Use your notes from the Work Backwards to prove activity to fill in the proof below that if the diagonals of a parallelogram are congruent, that parallelogram must be a rectangle
Given: ABCD is a parallelogram with AB parallel to CD and AD parallel to BC Diagonal AC is congruent to diagonal BD
Prove: ABCD is a rectangle (angles A, B, C and D are right angles),
12
I know 1 is congruent to 2 because it's the same segment. I know _3 is congruent to _14 because it's given. I know
5 is congruent to_6 because _7 is a parallelogram (given) and opposite sides of a parallelogram are congruent
Because_8 is congruent to 9 10 is congruent to _11 and
is congruent to 13 _, by the Side-Side
Side Triangle Congruence Theorem triangles_14
and 15
are congruent. Angle_16_ is congruent to angle
_17_because they are corresponding parts of two congruent triangles Angles 18
and
19 are right angles
because they're congruent and supplementary (because they are adjacent angles in a parallelogram). Congruent supplementary angles
must be right angles. Opposite angles in a parallelogram are congruent, so if angles_20 and 21 are right angles, then
angles 22 and 23
must be, too. I know 24 is a rectangle because angles_25
26
27
and
28 are all right angles, and a quadrilateral with four right angle is a rectangle.