1. Unit 6 Quadrilaterals Section 6.5 Properties of Rhombi and Squares

2. * * parallel congruent CONGRUENT congruent supplementary
parallelogram
4 equal sides
parallel
congruent *
CONGRUENT
congruent
supplementary
= 180
4 ≅ right
triangles
bisect each other *
ARE PERPENDICULAR

3. 180 – ____ – ____ =
32o
90o
58o
180 – ____ – ____ =
58o
58o
32o
90o

4. 180 – ____ – ____ = 32o 90o 58o 90o 60o 58o 58o 120o 30o 32o 90o 30o

5. diagonal
side 26
Diagonal
part 26 26 26 26 10 24

6. diagonal side side 26 _____ = _____ 2x + 4 4x – 4 26 26 –2x –2x 4 =
part
_____ = _____
2x + 4
4x – 4 26 12 26
–2x
–2x 12
4x – 4
= 12
4 =
2x – 4 26 +4 +4
2x + 4 10
2(4) + 4 = 8
= 2x 26 24 P=
4(12) 12
x = 4
= 48 2 2

7. diagonal side side 26 _____ = _____ 2x + 4 4x – 4 26 26 –2x –2x 4 =
part
_____ = _____
2x + 4
4x – 4 26 8 26
–2x
–2x 8
4x – 4
= 8
4 =
2x – 4 26 +4 +4
2x + 4 10
2(4) + 4 = 8
= 2x 26 24 P=
4(12) 12
x = 4
= 48 2 2
diagonal
part
whole diagonal 8 8
3y – 1 = 8 +1 +1
3y = 9 3 3
y = 3

8. diagonal side side 26 _____ = _____ 2x + 4 4x – 4 26 26 –2x –2x 4 =
part
_____ = _____
2x + 4
4x – 4 26 8 26
–2x
–2x 8
4x – 4
= 8
4 =
2x – 4 26 +4 +4
2x + 4 10
2(4) + 4 = 8
= 2x 26 24 P=
4(12) 12
x = 4
= 48 2 2
diagonal
part
diagonal
part
whole
diagonal
whole diagonal 13 8
a2 + b2 = c2 8
3y – 1 = 8 13 ? +1 +1 13
= c2 13 c
3y = 9 12 25
+ 144
= c2
P =
4(13) 3 3
169
= c2
y = 3
P = 52 5

9. parallelogram
rhombus
rectangle

10. parallel congruent are congruent congruent right angles supplementary
parallelogram
rhombus
rectangle 90 90
parallel
congruent
are congruent 90 90
congruent
right angles
supplementary
= 180

11. parallel congruent are congruent congruent right angles supplementary
parallelogram
rhombus
rectangle 90 90
parallel
congruent
are congruent 90 90
congruent
right angles 45 45
supplementary
4 ≅ right
isosceles
triangles
= 180
bisect each other 45
are congruent 45
are perpendicular

12. parallelogram
diagonals
bisect
rhombus
rectangle
diagonals
bisect
diagonals
bisect
and
diagonals
are ⊥
and
diagonals
are ≅
diagonals
bisect,
are ≅,
and are ⊥
square

13. 4 16
16 in
16 in 45 45
22.6 in
11.3 in
90o
45o 16 16
45o
90o
a2 + b2 = c2 45
= c2 45
256
+ 256
= c2
512
= c2 16