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Bell Ringer

Bell Ringer. Rhombi Rectangles & Squares. Rhombus. Definition:. A rhombus is a parallelogram with four congruent sides. Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. ≡. ≡.

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Bell Ringer

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  1. Bell Ringer Lesson 6-4: Rhombus & Square

  2. Rhombi Rectangles & Squares

  3. Rhombus Definition: A rhombus is a parallelogram with four congruent sides. • Opposite sides are parallel. • Opposite sides are congruent. • Opposite angles are congruent. • Consecutive angles are supplementary. • Diagonals bisect each other ≡ ≡ Since a rhombus is a parallelogram the following are true:

  4. Properties of a Rhombus Theorem: The diagonals of a rhombus are perpendicular. Theorem: Each diagonal of a rhombus bisects a pair of opposite angles.

  5. Rhombus Examples ..... Given: ABCD is a rhombus. Complete the following. • If AB = 9, then AD = ______. • If m<1 = 65, the m<2 = _____. • m<3 = ______. • If m<ADC = 80, the m<DAB = ______. • If m<1 = 3x -7 and m<2 = 2x +3, then x = _____. 9 units 65° 90° 100° 10

  6. Square Definition: A square is a parallelogram with four congruent angles and four congruent sides. • Opposite sides are parallel. • Four right angles. • Four congruent sides. • Consecutive angles are supplementary. • Diagonals are congruent. • Diagonals bisect each other. • Diagonals are perpendicular. • Each diagonal bisects a pair of opposite angles. Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals.

  7. Squares – Examples…... Given: ABCD is a square. Complete the following. • If AB = 10, then AD = _____ and DC = _____. • If CE = 5, then DE = _____. • m<ABC = _____. • m<ACD = _____. • m<AED = _____. 10 units 10 units 5 units 90° 45° 90°

  8. Rectangles

  9. Rectangles Definition: A rectangle is a parallelogram with four right angles. • Opposite sides are parallel. • Opposite sides are congruent. • Opposite angles are congruent. • Consecutive angles are supplementary. • Diagonals bisect each other. A rectangle is a special type of parallelogram. Thus a rectangle has all the properties of a parallelogram.

  10. A B E D C Properties of Rectangles Theorem: If a parallelogram is a rectangle, then its diagonals are congruent. Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles. Converse: If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle.

  11. A B 2 3 1 E 4 5 6 D C Examples……. • If AE = 3x +2 and BE = 29, find the value of x. • If AC = 21, then BE = _______. • If m<1 = 4x and m<4 = 2x, find the value of x. • If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6. x = 9 units 10.5 units x = 18 units m<1=50, m<3=40, m<4=80, m<5=100, m<6=40

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