7.4 Rhombus and SquareJan 25­10:43 AM
7.4 Rhombus 7.4 Square
opp sides //
opp angles ≅
consec. angles ≅
opp sides ≅
diags bisect
diags R
sides R ≅
diags ≅
Jan 25­10:29 AM
A rhombus is another special quadrilateral. A rhombus  is a quadrilateral with four congruent sides.
Jan 25­10:45 AM
Use the diagonals to determine whether a parallelogram  with the given vertices is a rectangle, rhombus, or square.  Give all the names that apply. W(0, 1), X(4, 2), Y(3, –2), Z(–1, –3)
W X
Y Z
7.4 Example
Jan 25­10:32 AM
A square is a quadrilateral with four right angles  and four congruent sides. Since a square is a  parallelogram, a rectangle, and a rhombus it  has the properties of all three.
EX. Determine if the conclusion is valid.  If not, tell what additional information is needed to make it valid. 
Conclusion: EFGH is a square.
Given:
Jan 25­10:32 AM
If XW = 13, then WZ = 13,  XZ = 13 root 2 and AZ = 13/2 root 2.
Find x if m<AZW = 3x + 15. 10
Find y if m<ZAY = 9y.10
A
Ex. Builders often use a square frame when building houses. 
If XW = 13, then WZ = _______, 
XZ = _______ and AZ = ______.
Find y if m∠ZAY = 9y. ______
Hint: Check answers by moving picture!!
7.4 Example
Rhombus follow up.gsp
Square follow up.gsp
Squares 4th period.docx
Free shipping and handling!
Only for $19.99
A parallelogram except with 4 congruent sides!
4in
4in
4in
4in
4in
4in
4in
4in
80°
80°
100°
100°
40°
40°
40°
40°
50°
50°
50°
50°
√32
√32
All sides congruent
Opp angles congruent
Diagonals are perpendicular
Seen our ad on T.V.? Watch it here on YouTube!
Squares, the simple shape.
Who likes to do a lot of math to figure out all the different measurements of shapes? With a square you can know most of the measurements just by knowing one diagonal and one side length! In a square all angles are equal so you know that all angles are 90 degrees. Also all sides are equal so you can know all of the side lengths if one side length is given. Diagonals are angle bisectors. Diagonals are perpendicular bisectors of each other too. So, the diagonals form 4 congruent triangles within the square. So you can know all sorts of measurements of a square with doing little to no math at all if you are given one side length and or diagonal!
SMART Notebook
Has 2 pairs of parallel sides
All sides are congruent to each other
All angles equal 90 degrees/are congruent
The diagonals create perpendicular bisectors
The diagonals also create angle bisectors
The diagonals form 2 congruent isosceles triangles
Base angles are congruent