Unit 6 Quadrilaterals Section 6.3 Properties of Rectangles

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Unit 6 Quadrilaterals Section 6.3 Properties of Rectangles

parallelogram 4 right angles

* * parallel congruent RIGHT ANGLES congruent supplementary parallelogram 4 right angles 90o 90o parallel congruent * 90o 90o RIGHT ANGLES congruent supplementary * = new rules – Review old properties first = 180 bisect each other * ARE CONGRUENT

R S U T _____ = _____ 6x + 3 7x – 2 –6x –6x 3 = 1x – 2 +2 +2 5 = x diagonal R S U T _____ = _____ 6x + 3 7x – 2 –6x –6x 3 = 1x – 2 +2 +2 5 = x

R S U T _____ = _____ 6y + 2 4y + 6 _____ = _____ 6x + 3 7x – 2 –4y diagonal Diagonal part R S *Since rectangle diagonals are = , all 4 parts are = to each other. U T _____ = _____ 6y + 2 4y + 6 _____ = _____ 6x + 3 7x – 2 –4y –4y –6x –6x 2y + 2 = 6 2y = 4 3 = 1x – 2 –2 –2 2 2 +2 +2 2y = 4 x y= 2 5 =

66 33 7(5) – 2 = 33 _____ = _____ 6x + 3 7x – 2 –6x –6x 6(5) + 3 = 33 +2 +2 5 = x

* * 66 8(4) + 3 = 35o 33 7(5) – 2 = 33 8x + 3 _____ + _____ = 90 Angle parts 66 * * 33 8(4) + 3 = 35o 33 33 33 33 7(5) – 2 = 33 8x + 3 _____ + _____ = 90 16x – 9 24x = 96 _____ = _____ 6x + 3 7x – 2 24 24 –6x –6x 6(5) + 3 = 33 24x – 6 = 90 3 = x – 2 +6 +6 x= 4 +2 +2 5 = x

* * * 90 - ___ = 47 43o 10x + 7 _____ = _____ 6x + 23 4x = 16 4 –6x 4 –7 –7 4x = 16 10(4) + 7 = 47

* * * * * * 90 - ___ = 47 43o 3(11) + 6 = 39o 10x + 7 6x + 23 4x = 16 _____ = _____ 3x + 6 _____ + _____ = 90 5x – 4 4 –6x 4 –6x 8x = 88 8 8 8x + 2 4x + 7 = 23 = 90 x= 4 –2 –7 –7 –2 x= 11 16 10(4) + 7 = 47 4x = 8x = 88

* 90 – ____ = 37o 8 cm 6 cm 10 cm 5 cm 53o 37o 6 cm 8 cm a2 + b2 = c2 82 + 62 = c2 6 cm ? 64 + 36 = c2 c 10 100 = c2

* * * 90 – ____ = 37o 8 cm 6 cm 10 cm 5 cm 53o 37o 6 cm 37o 106o 8 cm a2 + b2 = c2 8 cm 82 + 62 = c2 6 cm ? 64 + 36 = c2 c 37o 10 180 – ____ – ____ = 37o 106o 100 = c2