prove that opposite sides of a parallelogram are equal
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Let parallelogram ABCD, have sides such that AB is parallel to CD and AC is parallel to BD.
AB ll CD and AC ll BD --> Write the problem.
Draw line BD --> There is exactly one line through any two points.
angle ABD≅angle BDC --> Alternate Interior Angles Theorem.
angle ADB≅angle DBC --> Alternate Interior Angles Theorem.
BD=BD --> Reflexive Property of equality.
∆ABD≅∆BDC --> ASA Congruence Theorem.
AB=CD, AD=BC Corresponding Parts of Congruent Triangles are Congruent.
This is the proof of the theorem.
Hope it helps!
AB ll CD and AC ll BD --> Write the problem.
Draw line BD --> There is exactly one line through any two points.
angle ABD≅angle BDC --> Alternate Interior Angles Theorem.
angle ADB≅angle DBC --> Alternate Interior Angles Theorem.
BD=BD --> Reflexive Property of equality.
∆ABD≅∆BDC --> ASA Congruence Theorem.
AB=CD, AD=BC Corresponding Parts of Congruent Triangles are Congruent.
This is the proof of the theorem.
Hope it helps!
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