Question

The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent:

Answer 1

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Using a straightedge, extend segment AB and place point P above point B. By the same reasoning, extend segment AD and place point T to the left of point A. Angles BCD and PBC are congruent by the Alternate Interior Angles Theorem. Angles PBC and BAD are congruent by the ____________. By the Transitive Property of Equality, angles BCD and BAD are congruent. Angles ABC and BAT are congruent by the _____________. Angles BAT and CDA are congruent by the Corresponding Angles Theorem. By the Transitive Property of Equality, ∠ABC is congruent to ∠CDA. Consequently, opposite angles of parallelogram ABCD are congruent.

Answer 2

What theorems accurately complete the proof?


Corresponding Angles Theorem
Alternate Interior Angles Theorem

Alternate Interior Angles Theorem
Corresponding Angles Theorem

Corresponding Angles Theorem
Corresponding Angles Theorem

Alternate Interior Angles Theorem
Alternate Interior Angles Theorem

Answer 3

Given: segment A B is parallel to segment C D.
Prove: Alternate interior angles are congruent

∠2 and ∠6 are corresponding angles. they are congruent.
∠2 and ∠4 are vertically opposite angles. they are congruent.
∠4 is congruent to ∠6 by transitive property of equality

Answer 4

above is your proof.

yes, axioms we cannot prove. but we can prove this if we dont consider it as an axiom, and consider "corresponding angles property" as an axiom !!

Answer 5

medal please

Answer 6

wait wait... so c?

Answer 7

@jordanloveangel

Answer 8

yes

Answer 9

thank you !!

Answer 10

yc

Answer 11

do you mind helping me with some more? its just one more and the other two i just wanna double check?

Answer 12

yes sure

Answer 13

According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Construct diagonal A C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. Angles BAC and DCA are congruent by the Alternate Interior Angles Theorem. Angles BCA and DAC are congruent by the same theorem. __________. By CPCTC, opposite sides AB and CD, as well as sides BC and DA, are congruent.

Which sentence accurately completes the proof?

Triangles BCA and DAC are congruent according to the Angle-Angle-Side (AAS) Theorem.
Triangles BCA and DAC are congruent according to the Angle-Side-Angle (ASA) Theorem.
Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent).
Angles BAD and ADC, as well as angles DCB and CBA, are supplementary by the Same-Side Interior Angles Theorem.

Answer 14

I believe its C) Angles ABC and CDA are congruent according to a property of parallelograms (opposite angles congruent). most likey tho

Answer 15

i found it easier to screenshot

Answer 16

@jordanloveangel

Answer 17

yes

Answer 18

it is correct?

Answer 19

yes

Answer 20

okay las one to check

Answer 21

@jordanloveangel

Answer 22

First one was wrong just saying for future users!