Question

The figure below shows a parallelogram ABCD.

The flow chart with missing reason proves that consecutive angles of a parallelogram add to 180°.

Which reason can be used to fill in the blank spaces?

a) Angle Addition Postulate

b) Definition of a Quadrilateral

c) Definition of Parallel Lines

d) Definition of a Parallelogram

Answer 1

@ganeshie8

Answer 2

This would be definition of parallel lines, right?

Answer 3

more approppriate here is this :-
d) Definition of a Parallelogram

Answer 4

Okay, thank you! What about this one:

The figure below shows rectangle ABCD.

The two-column proof with missing statement proves that the diagonals of the rectangle bisect each other.

Which statement can be used to fill in the blank space?


a) AB ≅ CD

b) BE ≅ AE

c) BE ≅ CE

d) BC ≅ AD

Answer 5

after blank, look at the next second step

Answer 6

Alternate interior angles theorem?

Answer 7

there we're using ASA to prove congrence

Answer 8

next to that step

Answer 9

Oh that step, okay.

Answer 10

look at those two triangles :-

\(\triangle ADE\) and \(\triangle CBE\)

Answer 11

BC = AD , by definition of parallelogram.

Answer 12

Got it, because the two sides are the same length - that makes sense!

Answer 13

yes ! opposite sides (BC and AD) are equal in a parallelogram

Answer 14

Thank you!!

Answer Choices (the question is the picture):

∡1 + ∡2 = ∡3 + ∡4

∡1 + ∡2 = 180 and ∡2 + ∡3 = 180

∡1 + ∡2 = ∡2 + ∡3

∡1 = ∡3

Answer 15

I have no idea how to do this, I don't even know where to start with this one

Answer 16

@ganeshie8

Answer 17

easy, just subtract \(\angle 2 \) both sides

Answer 18

so the last choice angle 1 = angle 3

Answer 19

Yes !

Answer 20

Thank you! Okay, how do I prove that the diagonals of the square bisect the interior angles of the figure attached?

Answer 21

easy, prove \(\triangle PQR \cong \triangle PSR\)

Answer 22

hold on, you wanto prove diagonals bisect the angles... let me think a bit

Answer 23

discard above

Answer 24

Okay, is there like a specific theorem or postulate we can use?

Answer 25

do this :-

1. prove \(\triangle PQT \cong \triangle RQT\)

2. then, by CPCTC, \(\angle PQT \cong \angle RQT\)

Answer 26

for 1, you can use SSS congruence. i need to go cya in an hour or so. good luck !

Answer 27

Okay, thank you!