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Section 8.4 Rhombuses, Rectangles and Squares

Section 8.4 Rhombuses, Rectangles and Squares. Quadrilaterals. A polygon with four sides. Parallelograms. Kites. Trapezoids. A quadrilateral with both pairs of opposite sides parallel and congruent . Rectangle. Rhombus. Isosceles Trapezoid. Right Trapezoid.

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Section 8.4 Rhombuses, Rectangles and Squares

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  1. Section 8.4 Rhombuses, Rectangles and Squares

  2. Quadrilaterals A polygon with four sides. Parallelograms Kites Trapezoids A quadrilateral with both pairs of opposite sides parallel and congruent. Rectangle Rhombus Isosceles Trapezoid Right Trapezoid A parallelogram with 4 congruent sides. A parallelogram with 4 right angles. Square A parallelogram with 4 congruent sides and 4 right angles.

  3. Parallelogram Theorems: • Thm. 8.3: If a quadrilateral is a parallelogram, then its opposite SIDES are • congruent. • Thm. 8.4: If a quadrilateral is a parallelogram, then its opposite ANGLES are • congruent. • Thm. 8. 5: If a quadrilateral is a parallelogram, then its consecutive angles are • SUPPLEMENTARY. • Thm. 8.6: If a quadrilateral is a parallelogram, then its diagonals bisect each • other. • Rhombus Theorems: • Thm. 8.11 A parallelogram is a rhombus if and only if its diagonals • are perpendicular. • Thm. 8.12 A parallelogram is a rhombus if and only if each diagonal • bisects a pair of opposite angles..

  4. Rectangle Theorems: • Thm. 8.13 A parallelogram is a rectangle if and only if its diagonals • are congruent. • REMEMBER:* The theorems that apply to parallelograms, ALSO apply to the special types of parallelograms – rhombus, rectangle and square.

  5. X W REMEMBER: All squares are rectangles, but NOT all rectangles are squares! Z Y If WXYZ is a square, then these sides are congruent, so this statement is SOMETIMES TRUE.

  6. Look at theorems for rhombuses. Thm 8.12, diagonals of rhombuses bisect opposite angles so: = 53°

  7. 34° Look at theorems for rectangles. Need angle TRQ to get to angle SRT: Rectangles have RIGHT angles so: = 90°- 34°= 56°

  8. 1 REMEMBER: Squares have ALL the theorems of parallelograms, rectangles and rhombuses! Thm 8.6 (diagonals bisect each other) means that KN = 1 ThenLN = 2 Thm 8.13 (diagonals are congruent for rectangles) means that LN = MP ThenMP = 2

  9. Homework Section 8-4 Pg. 537 – 538 3 – 6, 9 – 17, 20 – 24 even, 32 – 35, 38 – 41, 44 – 49

  10. Geometry – Classifying Quadrilaterals Quadrilaterals Parallelograms Rhombus A polygon with four sides. Kites Trapezoids A quadrilateral with both pairs of opposite sides parallel and congruent. A quadrilateral with 2 pairs of adjacent sides congruent and no opposite sides congruent. A quadrilateral with exactly 1 pair of parallel sides. Rectangle Isosceles Trapezoid Right Trapezoid A parallelogram with 4 right angles. A parallelogram with 4 congruent sides. A trapezoid whose 2 non-parallel sides are congruent. A trapezoid with exactly 2 right angles. Square A parallelogram with 4 congruent sides and 4 right angles.

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