Unit 6 Quadrilaterals Section 6.1 Properties of Parallelograms

parallel parallel congruent congruent supplementary bisect each other quadrilateral parallel parallel congruent congruent supplementary = 180 bisect each other

65o 6 cm 65o 115o 8 cm = 180 180 – _____ = 115o 65o

= 180 17 65o 14 6 cm 68o 65o 115o ___ = ___ 2a 34 ___ = ___ 8b 112 8 cm 2 2 = 180 8 8 a = 17 b = 14 180 – ____ = 115o 65o 180 – ____ = 112o 68o

65o 13 32.5 60 65o 55 = 180 = 180 180 – _____ = 115o 65o 2y = 65 5x = 65 2 2 5 5

65o = 180 13 10 32.5 40 60 65o 55 = 180 ___ + ___ = 180 3y 6x = 180 = 180 3y + 6(__) = 180 10 180 – _____ = 115o 65o ___ + ___ = 180 6x 12x 3y + 60 = 180 2y = 65 5x = 65 ___x = 180 18 –60 –60 2 2 5 5 18 18 3y = 120 3 3

_____ = _____ 7x 3x + 14 –3x –3x 4x = 14 4 4 x = 3.5 24.5 24.5 = 3(3.5) + 14 4 4 x = 3.5 24.5 24.5

_____ = _____ 7x 3x + 14 –3x –3x = 180 4x = 14 4 4 x = 3.5 24.5 24.5 2(27) – 3 = 180 4x = 14 = 3(3.5) + 14 4 4 5(27) – 6 x = 3.5 24.5 24.5 2z – 3 _____ + _____ = 180 5z – 6 7z = 189 51o 129o 7 7 7z – 9 = 180 51o 129o +9 +9 z = 27

4 4.5 ___ = ___ 6x 24 ___ = ___ 4y 18 6 6 4 4 x = 4 y = 4.5

4 4.5 12 12 ___ = ___ 6x 24 ___ = ___ 4y 18 6 6 4 4 x = 4 y = 4.5 4 + 8 4.5 3(4) 12 12 ___ = ___ 6x 24 ___ = ___ 4y 18 6 6 4 4 x = 4 y = 4.5 ____ = ____ 3w w + 8 – w –w 2w = 8 w = 4 2 2

4(4.5) – 9 4 4 + 8 4.5 3(4) 2(4.5) 12 12 ___ = ___ 6x 24 ___ = ___ 4y 18 9 18 6 6 4 4 x = 4 24 9 y = 4.5 4z – 9 ____ = ____ 2z ____ = ____ 3w w + 8 – 2z –2z – w –w 2z – 9 = 2w = 8 w = 4 +9 +9 2 2 2z = 9 2 2

𝑬𝑭 Opposite sides are parallel 𝑮𝑭 Opposite sides are congruent 𝑯𝑬 Diagonals bisect each other ∠𝑭𝑮𝑫 Opposite angles are congruent Consecutive angles are supp. ∠𝑫𝑬𝑭 ∠𝑫𝑮𝑭