Lesson 8-5. Rhombi and Squares. Transparency 8-5. 50. 3. ± 4. 52°. 104°. C. 5-Minute Check on Lesson 8-4. WXYZ is a rectangle. Find each value. 1. If ZX = 6x – 4 and WY = 4x + 14, find ZX. 2. If WY = 26 and WR = 3y + 4, find y. 3. If mWXY = 6a² - 6, find a.
Rhombi and Squares
5-Minute Check on Lesson 8-4
WXYZ is a rectangle. Find each value.
1. If ZX = 6x – 4 and WY = 4x + 14, find ZX.
2. If WY = 26 and WR = 3y + 4, find y.
3. If mWXY = 6a² - 6, find a.
RSTU is a rectangle. Find each value.
6. What are the coordinates of W if WXYZ is a rectangle and X(2,6), Y(4,3), and Z(1,1)?
Standardized Test Practice:
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Rhombus CharacteristicsAll Parallelogram Properties
All 4 Sides Congruent
Diagonals bisect a pair of opposite ’s
Diagonals form right angles with each other
Square CharacteristicsAll Parallelogram PropertiesAll Rectangle Properties
All Rhombus Properties
Diagonals divide into 4 congruent ∆’s
Use rhombus LMNP to find the value of y if m1 = y² - 54.
Diagonals of a rhombus are perpendicular.
Add 54 to each side.
Take the square root of each side.
Answer: The value of y can be 12 or –12.
Use rhombus LMNP to find mPNL if mMLP = 64
Opposite angles are congruent.
The diagonals of a rhombus bisect the angles.
Use rhombus ABCD and the given information to find the value of each variable.
Answer: 8 or –8
A square table has four legs that are 2 feet apart. The table is placed over an umbrella stand so that the hole in the center of the table lines up with the hole in the stand. How far away from a leg is the center of the hole?
Let ABCD be the square formed by the legs of the table. Since a square is a parallelogram, the diagonals bisect each other. Since the umbrella stand is placed so that its hole lines up with the hole in the table, the center of the umbrella pole is at point E, the point where the diagonals intersect. Use the Pythagorean Theorem to find the length of a diagonal.
The distance from the center of the pole to a leg is equal to the length ofExample 5-4b
Answer: The center of the pole is about 1.4 feet from a leg of a table.
Kayla has a garden whose length and width are each 25 feet. If she places a fountain exactly in the center of the garden, how far is the center of the fountain from one of the corners of the garden?
Answer: about 17.7 feet
4 sided polygon
4 interior angles sum to 360
4 exterior angles sum to 360
Legs are not Parallel
Leg angles are supplementary
Median is parallel to basesMedian = ½ (base + base)
Opposite sides parallel and congruent
Opposite angles congruent
Consecutive angles supplementary
Diagonals bisect each other
All sides congruent
Diagonals bisect opposite angles
Angles all 90°
Legs are congruent
Base angle pairs congruent
Diagonals are congruent
Diagonals divide into 4 congruent triangles