Transcript Lesson 6.2

Bellringer
 Can a triangle have the sides with the given
lengths? Explain
1. 8mm, 6mm, 3mm
2. 5ft, 20ft, 7ft
3. 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.
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 sameside interior angles, so they are supplementary.
𝑚∠𝑆 + 112 = 180
−112 − 112
𝑚∠𝑆 = 68
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
14𝑦 − 32 + 5 = 5𝑦
14𝑦 − 27 = 5𝑦
−27 = −9𝑦
𝑦=3
𝑥 = 7𝑦 − 16
𝑥 = 7 3 − 16
𝑥 = 21 − 16
𝑥=5
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.
BD  DF
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