Question

I need someone to check my answers for geometry! Will fan+medal!! Thanks!

Write an indirect proof to show that a rectangle has congruent diagonals. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.

Answer 1

For this, I wrote: I will create the rectangle RECT. It will be given that quadrilateral RECT is a rectangle. I will prove that rectangle RECT is a parallelogram with congruent diagonals. It is given that quadrilateral RECT is a rectangle. By the definition of a rectangle, all four angles will measure 90 degrees. Any two adjacent angles in rectangle RECT add up to 180 degrees since 90 degrees + 90 degrees = 180 degrees. These adjacent angles are same-side interior angles because they are located inside, and on the same side of two lines intersected by a transversal. Therefore, segment ER is parallel to segment CT and segment EC is parallel to segment RT. Segment ER is parallel to segment CT by the converse of the Same-Side Interior Angles Theorem. Quadrilateral RECT is then a parallelogram by definition of a parallelogram. I will now construct the diagonals ET and CR. Since angle CTR and angle TRE both measure 90 degrees, these angles are congruent according to the definition of congruence. Because RECT is a parallelogram, the opposite sides will be parallel. Therefore, segment ER will be congruent to segment CT. Segment TR is congruent to itself by the Reflexive Property of Equality. The two corresponding, congruent sides (ER and CT with TR and TR) will be joined by a corresponding pair of congruent angles (angle ERT and angle CTR). The SAS (side angle side) Theorem says triangle ERT is congruent to triangle CTR. Because of CPCTC, (corresponding parts of congruent triangles are congruent) the diagonals ET and CR are congruent.

Answer 2

i am flvs also

Answer 3

@ganeshie8 Is this a good answer?

Answer 4

@pinkiepieinthetardis that's cool! are you on geometry right now?

Answer 5

@paki