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. (10 points)

answer:

given a rectangle, prove that the diagonals are congruent.

given: rectangle abcd

prove: segment ac ≅ segment bd

since abcd is a rectangle, it is also a parallelogram.

since abcd is a parallelogram, segment ab ≅ segment dc because opposite sides of a parallelogram are congruent

bc ≅ bc by the reflexive property of congruence.

furthermore, ∠abc and ∠dcb are right angles by the definition of rectangle.

∠abc ≅ ∠dcb since all right angles are congruent.

summary

ab ≅ segment dc

∠abc ≅ ∠dcb

bc ≅ bc

therefore, by sas, triangle abc ≅ triangle dcb.

since triangle abc ≅ triangle dcb, segment ac ≅ segment bd

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.