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Bellringer Can a triangle have the sides with the given lengths? Explain 8mm, 6mm, 3mm 5ft, 20ft, 7ft 3m, 5m, 8m
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6-2 Properties of Parallelograms
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Theorems Theorem 6-1: Opposite sides of a parallelogram are congruent
Theorem 6-2: Opposite angles of a parallelogram are congruent Theorem 6-3: The diagonals of a parallelogram bisect each other.
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ππ
=3π₯β15 ππ
=3 18 β15 ππ
=54β15 ππ
=39 ππ=2π₯+3 ππ=2 18 +3 ππ=36+3 ππ=39
3π₯β15=2π₯+3 β2π₯ β2π₯ 1π₯ β15=3 π₯=18 ππ
=3π₯β15 ππ
=3 18 β15 ππ
=54β15 ππ
=39 ππ=2π₯+3 ππ= ππ=36+3 ππ=39
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*Consecutive angles of a parallelogram are same-side interior angles, so they are supplementary.
πβ π+112=180 β112 β112 πβ π=68
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πβ π΅=π₯+15 πβ π΅=60+15 πβ π΅=75 πβ π΄=180βπβ π΅ πβ π΄=180β75 πβ π΄=105 πππβπ=π+ππ
____βπ βπ_____ πππβππ=ππ βπππ βπππ βππ=βπππ βπ βπ π=ππ πβ π΅=π₯+15 πβ π΅=60+15 πβ π΅=75 πβ π΄=180βπβ π΅ πβ π΄=180β75 πβ π΄=105
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2π₯+5=5π¦ π₯=7π¦β16 2(7π¦β16)+5=5π¦ π₯=7π¦β16 14π¦β32+5=5π¦ π₯=7 3 β16 14π¦β27=5π¦
β27=β9π¦ π¦=3 π₯=7π¦β16 π₯=7 3 β16 π₯=21β16 π₯=5 Systems of Equations
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Theorem 6-4: If three (or more) parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal.
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π¦=11 πβ πΈ=πβ πΊ=70 πβ πΉ=πβ π»=110 π=16 π=14 πΈπ»=7.5
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Practice!! Pg #1-22 and 44-52
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