Bellringer Can a triangle have the sides with the given lengths? Explain 8mm, 6mm, 3mm 5ft, 20ft, 7ft 3m, 5m, 8m

6-2 Properties of Parallelograms

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.

𝑄𝑅=3𝑥−15 𝑄𝑅=3 18 −15 𝑄𝑅=54−15 𝑄𝑅=39 𝑃𝑆=2𝑥+3 𝑃𝑆=2 18 +3 𝑃𝑆=36+3 𝑃𝑆=39 3𝑥−15=2𝑥+3 −2𝑥 −2𝑥 1𝑥 −15=3 +15 +15 𝑥=18 𝑄𝑅=3𝑥−15 𝑄𝑅=3 18 −15 𝑄𝑅=54−15 𝑄𝑅=39 𝑃𝑆=2𝑥+3 𝑃𝑆=2 18 +3 𝑃𝑆=36+3 𝑃𝑆=39

*Consecutive angles of a parallelogram are same-side interior angles, so they are supplementary. 𝑚∠𝑆+112=180 −112 −112 𝑚∠𝑆=68

𝑚∠𝐵=𝑥+15 𝑚∠𝐵=60+15 𝑚∠𝐵=75 𝑚∠𝐴=180−𝑚∠𝐵 𝑚∠𝐴=180−75 𝑚∠𝐴=105 𝟏𝟑𝟓−𝒙=𝒙+𝟏𝟓 ____−𝒙 −𝒙_____ 𝟏𝟑𝟓−𝟐𝒙=𝟏𝟓 −𝟏𝟑𝟓 −𝟏𝟑𝟓 −𝟐𝒙=−𝟏𝟐𝟎 −𝟐 −𝟐 𝒙=𝟔𝟎 𝑚∠𝐵=𝑥+15 𝑚∠𝐵=60+15 𝑚∠𝐵=75 𝑚∠𝐴=180−𝑚∠𝐵 𝑚∠𝐴=180−75 𝑚∠𝐴=105

2𝑥+5=5𝑦 𝑥=7𝑦−16 2(7𝑦−16)+5=5𝑦 𝑥=7𝑦−16 14𝑦−32+5=5𝑦 𝑥=7 3 −16 14𝑦−27=5𝑦 −27=−9𝑦 𝑦=3 𝑥=7𝑦−16 𝑥=7 3 −16 𝑥=21−16 𝑥=5 Systems of Equations

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.

𝑦=11 𝑚∠𝐸=𝑚∠𝐺=70 𝑚∠𝐹=𝑚∠𝐻=110 𝑎=16 𝑏=14 𝐸𝐻=7.5

Practice!! Pg. 297-300 #1-22 and 44-52