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Lesson 8-5

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 mWXY = 6a² - 6, find a.

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Lesson 8-5

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  1. Lesson 8-5 Rhombi and Squares

  2. 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 mWXY = 6a² - 6, find a. RSTU is a rectangle. Find each value. 4. mVRS 5. mRVU 6. What are the coordinates of W if WXYZ is a rectangle and X(2,6), Y(4,3), and Z(1,1)? X W R Y Z S R V 38° U T Standardized Test Practice: (1,4) (1,-4) (-1,-4) (-1,4) A B C D Click the mouse button or press the Space Bar to display the answers.

  3. Objectives • Recognize and apply the properties of rhombi • All Parallelogram Properties • All 4 Sides Congruent • Diagonals bisect a pair of opposite ’s • Diagonals form right angles with each other • Recognize and apply the properties of squares • All Parallelogram Properties • All Rectangle Properties • All Rhombus Properties • Diagonals divide into 4 congruent ∆’s (45-45-90)

  4. Vocabulary • Rhombus – quadrilateral with all four sides congruent • Square – a quadrilateral that is both a rhombus and a rectangle

  5. Rhombi and Squares A B Rhombus CharacteristicsAll Parallelogram Properties All 4 Sides Congruent Diagonals bisect a pair of opposite ’s Diagonals form right angles with each other C D A B Square CharacteristicsAll Parallelogram PropertiesAll Rectangle Properties All Rhombus Properties Diagonals divide into 4 congruent ∆’s D C

  6. N EXAMPLE 1 Example 5-2a Use rhombus LMNP to find the value of y if m1 = y² - 54. Diagonals of a rhombus are perpendicular. Substitution Add 54 to each side. Take the square root of each side. Answer: The value of y can be 12 or –12.

  7. N Answer: EXAMPLE 2 Example 5-2c Use rhombus LMNP to find mPNL if mMLP = 64 Opposite angles are congruent. Substitution The diagonals of a rhombus bisect the angles.

  8. a. b. Answer: EXAMPLE 3 Example 5-2e Use rhombus ABCD and the given information to find the value of each variable. Answer: 8 or –8

  9. Quadrilateral Characteristics Summary Convex Quadrilaterals 4 sided polygon 4 interior angles sum to 360 4 exterior angles sum to 360 Parallelograms Trapezoids Bases Parallel 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 Rectangles Rhombi IsoscelesTrapezoids All sides congruent Diagonals perpendicular Diagonals bisect opposite angles Angles all 90° Diagonals congruent Legs are congruent Base angle pairs congruent Diagonals are congruent Squares Diagonals divide into 4 congruent triangles

  10. Summary & Homework • Summary: • A rhombus is a quadrilateral with each side congruent, diagonals that are perpendicular, and each diagonal bisecting a pair of opposite angles. • A quadrilateral that is both a rhombus and a rectangle is a square. • Homework: • pg 434 (12-19)

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