Question

Write a 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

@AlexandervonHumboldt2

Answer 2

easy:

Answer 3

now we have that AD=BC, DC=AB, <D=<A=<B=<C.

Answer 4

thus triangle ADC=triangle BDC. Thus DB=AC

Answer 5

triangle ADC=BDC by 2 sides and an angle

Answer 6

What are the reasons for all of that? I can't just state facts with a proof, can I?

Answer 7

AD=BC, DB=AC by because it is a rectangular.

Answer 8

DC=DC by reflexive property

Answer 9

so the definition of a rectangle

Answer 10

yes

Answer 11

all angles of rectangular are 90

Answer 12

thus they are all congruent between themselves.

Answer 13

now we have enough info to say that the triangles are congruent by 2 pair sides and 1 pair angles.

Answer 14

so SAS for the triangles?

Answer 15

yes

Answer 16

we use SAS to say that they are congruent.

Answer 17

okay. is that all there is, what you already listed?

Answer 18

well ok let me combine it all:
AD=BC, DB=AC by because it is a rectangular.
DC=DC by reflexive property
all angles of rectangular are 90°. <D=<A=<B=<C.
Thus the triangles are congruent by SAS. Thus AC=BD.

Answer 19

Thank you so much!

Answer 20

:)