Question

Oscar wrote a partial narrative proof to prove AB ? CD and BC ? AD. Given: ABCD is a parallelogram. Prove: AB ? CD and BC ? AD Use the information in the boxes at the bottom of the page to fill in the blanks to complete the proof below. It is given that ABCD is a parallelogram. Diagonal AC is drawn and angles 1, 2, 3, and 4 are labeled. Because opposite sides of a parallelogram are parallel, then we know . Also, because alternate interior angles are congruent. By the , AC ? AC. Therefore, ?BAC ? ?DCA by . Finally, AB ? CD and BC ? AD because . Angle-Side-Angle | Substitution Symmetric Property | ?1 ? ?4 and ?2 ? ?3 AB || CD and AD || BC | Reflexive Property Side-Angle-Side | ?1 ? ?3 and ?2 ? ?4 Transitive Property | CPCTC AB || AD and DC || BC | Side-Side-Side

          Oscar wrote a partial narrative proof to prove AB ? CD and BC ? AD.

Given: ABCD is a parallelogram.

Prove: AB ? CD and BC ? AD

Use the information in the boxes at the bottom of the page to fill in the blanks to complete the proof below.

It is given that ABCD is a parallelogram. Diagonal AC is drawn and angles 1, 2, 3, and 4 are labeled. Because opposite sides of a parallelogram are parallel, then we know . Also, because alternate interior angles are congruent. By the , AC ? AC. Therefore, ?BAC ? ?DCA by . Finally, AB ? CD and BC ? AD because .

Angle-Side-Angle | Substitution
Symmetric Property | ?1 ? ?4 and ?2 ? ?3
AB || CD and AD || BC | Reflexive Property
Side-Angle-Side | ?1 ? ?3 and ?2 ? ?4
Transitive Property | CPCTC
AB || AD and DC || BC | Side-Side-Side

Oscar wrote a partial narrative proof to prove AB ? CD and BC ? AD.

Given: ABCD is a parallelogram.

Prove: AB ? CD and BC ? AD

Use the information in the boxes at the bottom of the page to fill in the blanks to complete the proof below.

It is given that ABCD is a parallelogram. Diagonal AC is drawn and angles 1, 2, 3, and 4 are labeled. Because opposite sides of a parallelogram are parallel, then we know . Also, because alternate interior angles are congruent. By the , AC ? AC. Therefore, ?BAC ? ?DCA by . Finally, AB ? CD and BC ? AD because .

Angle-Side-Angle | Substitution
Symmetric Property | ?1 ? ?4 and ?2 ? ?3
AB || CD and AD || BC | Reflexive Property
Side-Angle-Side | ?1 ? ?3 and ?2 ? ?4
Transitive Property | CPCTC
AB || AD and DC || BC | Side-Side-Side

Added by Mar W.

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