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Given: ABCD is a parallelogram.

Prove: AB = CD and BC = DA

Answers are in the image.

Proving the Parallelogram Side Theorem

Given: ABCD is a parallelogram

Prove: AB = CD and BC = DA

Angles Segment Statements Reasoning

LBAC

LBCA

LDAC

LDCA

Statements:

1. ABCD is a parallelogram

2. AB || CD (draw AC)

3. LBCA and LDAC are alternate interior angles

4. LBCA = LDAC (alternate interior angles theorem)

5. LBCA and LBAC are alternate interior angles

6. LDAC and LDCA are alternate interior angles

7. AB = CD (corresponding angles are congruent)

8. BC = DA (corresponding angles are congruent)

This proof is complete.

Intro

Final

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02:19

Anyone got answers? Need help proving the Parallelogram Diagonal Theorem.

Given: ABCD is a parallelogram. Diagonals AC and BD intersect at E.Prove: AE = CE and BE = DE.

Angles Segments Triangles Statements ReasonsABAEBCBECEDADE

Statements:1. ABCD is a parallelogram.2. CD = AB.3. AB || CD.

Reasons:1. Given.2. Parallelogram side theorem.3. Definition of parallelogram.

Correctly assemble the next statement.

Intro

02:56

Given: ABCD is a parallelogramProve: AB = CD and BC = DA

Move statements and reasons to the table to complete the proof:

Statements Reasons————————————————–ABCD is a parallelogram GivenDA || BC and AB || CD Definition of a parallelogramâˆ ACD â‰… âˆ CAB and âˆ BCA â‰… âˆ DAB Alternate interior angles theoremAC = AC Reflexive propertyAB = CD and BC = DA CPCTC (Corresponding Parts of Congruent Triangles are Congruent)âˆ DAC â‰… âˆ CAB ASA (Angle-Side-Angle)âˆ BCH â‰… âˆ CDA ASA (Angle-Side-Angle)âˆ BAC â‰… âˆ BCD Vertical angles are congruentâˆ ARD â‰… âˆ BCD Vertical angles are congruent

04:16

Please Help!!

Given: ABCD is a parallelogram.Prove: AB is congruent to CD and BC is congruent to DA.Proving the Parallelogram Side Theorem

Given: ABCD is a parallelogram Prove: AB = CD and BC = DA

Angles Segments Angles Statements ReasonsLBACLBCALDACLDCA

StatementsReasonsHintIntro

02:49

Given: ABCD is a parallelogramProve: âˆ BCD â‰… âˆ DAB

Statement Reason 1. ABCD is a parallelogram Given 2. âˆ BCD â‰… âˆ DAB Alternate interior angles of a parallelogram are congruent 3. âˆ LADB = âˆ LDBC; âˆ LABD = âˆ LDCB Corresponding angles of a parallelogram are congruent 4. âˆ BCD â‰… âˆ DAB Transitive property of congruence

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