Question

Proving the Single Opposite Side Pair Theorem

Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
ZDAC
А
Statements
Reasons
B
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.

Answer 1

Picture Down Below

Step-by-step explanation:

Answer 2

9514 1404 393

Step-by-step explanation:

1. AD ≅ BC, AD ║ BC . . . . given

2. ∠DAC ≅ ∠BCA . . . . alternate interior angles theorem

3. AC ≅AC . . . . reflexive property

4. ΔDAC ≅ ΔBCA . . . . SAS postulate

5. AB ≅ CD, ∠BAC ≅ ∠DCA . . . . CPCTC

6. AB ║ CD . . . . converse of alternate interior angles theorem

7. ABCD is a parallelogram . . . . definition of a parallelogram (has 2 pairs of parallel & congruent sides)

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We don't know what your tiles/choices are for statements or reasons. We have shown the triangles are congruent, so their corresponding parts (sides/angles) are congruent. That lets us claim opposite sides are congruent and parallel. YMMV