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Mathematics 36 Online
OpenStudy (mack):

The following is an incomplete paragraph proving that the opposite sides of parallelogram ABCD are congruent. According to the given information, line AB|| line DC and line BC|| line AD. Construct diagonal A C with a straightedge. It is congruent to itself by the reflective property of equality. ____________. Angles BCA and DAC are congruent by the same reasoning. Triangles BCA and DAC are congruent according to the ASA theorem. By CPCTC, opposite sides AB and CD, as well as sides BC and DA are congruent. Which sentence accurately completes the proof?

OpenStudy (mack):

/Users/MackaylaMelendez/Downloads/IMG_6016.JPG

OpenStudy (mack):

/Users/MackaylaMelendez/Downloads/IMG_6017.JPG

OpenStudy (mathstudent55):

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OpenStudy (mathstudent55):

The figure above shows all the statements shown below. According to the given information, line AB|| line DC and line BC|| line AD. Construct diagonal A C with a straightedge. It is congruent to itself by the reflective property of equality. ____________. Angles BCA and DAC are congruent by the same reasoning.

OpenStudy (mathstudent55):

The blank statement is still not known.

OpenStudy (mathstudent55):

Look at the very next statement in the proof. "Triangles BCA and DAC are congruent according to the ASA theorem." The statements up to that point were written to prove that the triangles are congruent. The triangles were proved congruent using ASA. The figure shows one side congruent to one side. It also shows one angle congruent to one angle. That means out of ASA, we have (before the blank statement) AS. We are missing the second "A" of ASA. Also, notice that the first statement after the blank statement states "by the same reasoning." That means the blank statement must be that a pair of angles is congruent and the reason is the same reason used to state that angles BCA and DAC are congruent.

OpenStudy (mathstudent55):

Look at the triangles that are proved congruent, and figure out which other pair of congruent angles you need to prove those triangles congruent with ASA. Then figure out the reason you can state these angles are congruent.

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