Geometry Angles Parallel Lines Triangles Quadrilaterials

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Presentation transcript:

Geometry Angles Parallel Lines Triangles Quadrilaterials Parallelograms Area Circles Volume http://www.mcescher.com/Gallery/back-bmp/LW389.jpg

Types of Angles Classification Acute: all angles are less than 90° Obtuse: one angle is greater than 90° Right: has one angle equal to 90° Complementary: the sum of two angles is 90° Supplementary: the sum of two angles is 180° Adjacent: angles that share a side Linear Pair: angles that are both supplementary and adjacent

Congruent Angle Pairs formed by Parallel Lines Alternate interior angles <3 & <6, <4 & < 5 Alternate exterior angles <1 & <8, <2 & <7 Corresponding angles <1 & <5, <2 & <6, <3 & <7, <4 & <8 Vertical angles <1 & <4, <2 & <3, <5 & <8, <6 & <7 1 2 3 4 5 6 7 8

Supplementary Angle Pairs formed by Parallel Lines Angles that are both on the same side of the transversal and either both interior or exterior <3 & <5, <4 & < 6, <1 & <7, <2 & < 8 Linear Pair <1 & <2, <2 & <4, <3 & <4, <1 & <3, <5 & <6, <6 & <8, <7 & <8, <5 & <7 1 2 3 4 5 6 7 8

Polygons The sum of the interior angles: (n - 2)(180°) Classified by number of sides (n) Triangle (3) Quadrilateral (4) Pentagon (5) Hexagon (6) Heptagon (7) Octagon (8) Nonagon (9) Decagon (10) Regular Polygon: all sides are congruent

Triangles The sum of the angles in a triangle is 180° a – b < third side < a + b The sum of the two remote interior angles is equal to the exterior angles Types: Scalene Isosceles Equilateral Right Two sides are equal One Right angle All sides are equal No sides are equal

QUADRILATERALS TRAPEZOIDS Only one pair of PARALLELOGRAM Opposite sides parallel PARALLELOGRAM Both pairs of opposite sides are parallel ROMBUS 4 equal sides RECTANGLE 4 right angles ISOSCLES TRAPEZOID A trapezoid that has two equal sides SQUARE Both a rhombus and a rectangle

Properties of Parallelograms Diagonals bisect each other Opposite sides are congruent Opposite angles are congruent Consecutive angles are supplementary Diagonals form two congruent triangles Diagonals are perpendicular to each other Diagonals bisect their angles Diagonals are congruent to each other

Area ½bh bh lw ½(b1 + b2 ) s2

Circles Exact: express in terms of π Circumference C = 2πr or C = πd A = πr2 Exact: express in terms of π Approximate: use an approximation of π (3.14)

Volume General Formula: V = (area of base)(height) πr2h πr2h lwh πr3 Bh