Question

Zinnia wrote the following proof to show that the diagonals of rectangle ABCD are congruent.

Zinnia’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: DC = DC (reflexive property of equality)
Statement 4: Triangle ADC and BCD are congruent (by ASA postulate)
Statement 5: AC = BD (by CPCTC)
Which statement in Zinnia’s proof has an error?

Statement 1

Statement 4

Statement 3

Statement 2

Answer 1

tips?

Answer 2

SAS again

Answer 3

Statement 4 is flawed

Answer 4

First off, that's not a rectangle...

Answer 5

Are you sure you didn't copy/paste the wrong question?

Answer 6

`opps

Answer 7

A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram.

Side AB is parallel to side DC so the alternate interior angles, angle ABD and angle BDC are congruent. Side AB is equal to side DC and DB is the side common to triangles ABD and BCD. Therefore, the triangles ABD and BCD are congruent by SSS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.
Which statement best describes a flaw in the student’s proof?

Angle DBC and angle ADB form a pair of vertical angles which are congruent.

Triangles ABD and CDB are congruent by the SAS postulate.

Triangles ABD and BCD are congruent by the AAS postulate.

Angle DBC and angle ADB form a pair of corresponding angles which are congruent.

Answer 8

SAS still

Answer 9

wait

Answer 10

yeah

Answer 11

SAS

Answer 12

All of the other statements are basically invalid

Answer 13

I agree. The student should have used SAS instead of SSS.

Answer 14

k

Answer 15

last one for the day