Section 8.4 Rhombuses, Rectangles and Squares. Rhombus Quadrilaterals Parallelograms KitesTrapezoids Rectangle Square Isosceles Trapezoid Right Trapezoid.

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Presentation transcript:

Section 8.4 Rhombuses, Rectangles and Squares

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

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 A parallelogram is a rhombus if and only if its diagonals are perpendicular. Thm A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles..

 Rectangle Theorems: Thm 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.

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

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

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

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

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

Quadrilaterals KitesTrapezoids Rectangle Square Isosceles Trapezoid Right Trapezoid A polygon with four sides. 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. A parallelogram with 4 congruent sides. A parallelogram with 4 right angles. A trapezoid whose 2 non-parallel sides are congruent. A parallelogram with 4 congruent sides and 4 right angles. A trapezoid with exactly 2 right angles. Geometry – Classifying Quadrilaterals ParallelogramsParallelograms RhombusRhombus