Question

8. In quadrilateral ABCD, AD is congruent to BC, and AD is parallel to BC. Andre has written a proof to show that ABCD is a parallelogram. Fill in the blanks to complete the proof.
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Answer 1

The correct choices to fill the blanks are listed below:

1. AD
2. BC
3. AC
4. CBA
5. angle BAC
6. CD

How to prove that a quadrilateral is a parallelogram

In this question we should fill the blanks based all information related to Euclidean geometry, especially concepts related to angles, triangles, parallelism and quadrilaterals.

The complete paragraph is shown below:

Since AD is parallel to BC, alternate interior angles.

AD and BC are congruent.

AC is congruent to AC since segments are congruent to themselves.

Along with the given information that AD is congruent to BC, triangle ADC is congruent to triangle CBA by the Side-Angle-Side Triangle Congruence.

Since the triangles are congruent, all pairs of corresponding angles are congruent, so angle DCA is congruent to angle BAC.

Since those alternate interior angles are congruent. AB must be parallel to CD.

Since we define a parallelogram as a quadrilateral with both pairs of opposite sides parallel, ABCD is a parallelogram.

To learn more on quadrilaterals, we kindly invite to check this verified question: brainly.com/question/25240753