1. Unit 6 Quadrilaterals Section 6.3 Properties of Rectangles

2. parallelogram
4 right angles

3. * * 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

4. 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

5. 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 =

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

7. * * 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

8. * * * 90 - ___ = 47 43o 10x + 7 _____ = _____ 6x + 23 4x = 16 4 –6x 4–7 –7
4x = 16
10(4) + 7 = 47

9. * * * * * * 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

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

11. * * * 90 – ____ = 37o 8 cm 6 cm 10 cm 5 cm 53o 37o 6 cm 37o 106o 8 cm
a2 + b2 = c2
8 cm
= c2
6 cm ? 64
+ 36
= c2 c
37o 10
180 – ____ – ____ =
37o
106o
100
= c2