The figure below shows a rectangle abcd having diagonals ac and db: a rectangle abcd is shown with diagonals ac and bd. jimmy wrote the following proof to show that the diagonals of rectangle abcd are congruent: jimmy's proof: statement 1: in triangle adc and bcd, ad = bc (opposite sides of a rectangle are congruent) statement 2: angle adc = angle bcd (angles of a rectangle are 90°) statement 3: statement 4: triangle adc and bcd are congruent (by sas postulate) statement 5: ac = bd (by cpctc) which statement below completes jimmy's proof?

Statement 3: DC=CD (Common)

Step-by-step explanation:

According from the  statement given, consider ΔADC and ΔBCD, we get

AD=BC(opposite sides of a rectangle are congruent)

∠ADC=∠BCD(angles of a rectangle are 90°)

DC=CD(Common)

Thus, by SAS rule, ΔADC≅ΔBCD and by CPCTC AC=BD.

Thus, Statement 3 that is using the common sides of the triangle jimmy can prove the proof.

Answer

Statement 3: The side BC = BC (common side for ΔADC and ΔBCD)

Solution

Rectangle ABCD having diagonals AC and DB:  

proof

Statement 1: In triangle ADC and BCD, AD = BC (opposite sides of a rectangle are congruent)

Statement 2: Angle ADC = Angle BCD (angles of a rectangle are 90°)  

Statement 3: The side BC = BC (common side for ΔADC and ΔBCD)

Statement 4: Triangle ADC and BCD are congruent (by SAS postulate) Statement 5: AC = BD (by CPCTC)

The statement 3 completes Jimmy's proof.

it's

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.