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# Geometry

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### Geometry

1. 1. Geometry <ul><li>Angles </li></ul><ul><li>Parallel Lines </li></ul><ul><li>Triangles </li></ul><ul><li>Quadrilaterials </li></ul><ul><li>Parallelograms </li></ul><ul><li>Area </li></ul><ul><li>Circles </li></ul><ul><li>Volume </li></ul>
2. 2. Types of Angles <ul><li>Classification </li></ul><ul><ul><li>Acute: all angles are less than 90 ° </li></ul></ul><ul><ul><li>Obtuse: one angle is greater than 90 ° </li></ul></ul><ul><ul><li>Right: has one angle equal to 90 ° </li></ul></ul><ul><li>Complementary: the sum of two angles is 90 ° </li></ul><ul><li>Supplementary: the sum of two angles is 180 ° </li></ul><ul><li>Adjacent: angles that share a side </li></ul><ul><li>Linear Pair: angles that are both supplementary and adjacent </li></ul>
3. 3. Congruent Angle Pairs formed by Parallel Lines <ul><li>Alternate interior angles </li></ul><ul><li><3 & <6, <4 & < 5 </li></ul><ul><li>Alternate exterior angles </li></ul><ul><li><1 & <8, <2 & <7 </li></ul><ul><li>Corresponding angles </li></ul><ul><li><1 & <5, <2 & <6, <3 & <7, <4 & <8 </li></ul><ul><li>Vertical angles </li></ul><ul><li><1 & <4, <2 & <3, <5 & <8, <6 & <7 </li></ul>1 2 3 4 5 6 7 8
4. 4. <ul><li>Angles that are both on the same side of the transversal and either both interior or exterior </li></ul><ul><li><3 & <5, <4 & < 6, <1 & <7, <2 & < 8 </li></ul><ul><li>Linear Pair </li></ul><ul><li><1 & <2, <2 & <4, <3 & <4, <1 & <3, </li></ul><ul><li><5 & <6, <6 & <8, <7 & <8, <5 & <7 </li></ul>Supplementary Angle Pairs formed by Parallel Lines 1 2 3 4 5 6 7 8
5. 5. Polygons <ul><li>The sum of the interior angles: (n - 2)(180°) </li></ul><ul><li>Classified by number of sides (n) </li></ul><ul><ul><li>Triangle (3) </li></ul></ul><ul><ul><li>Quadrilateral (4) </li></ul></ul><ul><ul><li>Pentagon (5) </li></ul></ul><ul><ul><li>Hexagon (6) </li></ul></ul><ul><ul><li>Heptagon (7) </li></ul></ul><ul><ul><li>Octagon (8) </li></ul></ul><ul><ul><li>Nonagon (9) </li></ul></ul><ul><ul><li>Decagon (10) </li></ul></ul><ul><li>Regular Polygon: all sides are congruent </li></ul>
6. 6. Triangles <ul><li>The sum of the angles in a triangle is 180 ° </li></ul><ul><li>a – b < third side < a + b </li></ul><ul><li>The sum of the two remote interior angles is equal to the exterior angles </li></ul><ul><li>Types: </li></ul>Two sides are equal One Right angle All sides are equal Scalene Isosceles Equilateral Right No sides are equal
7. 7. QUADRILATERALS PARALLELOGRAM Both pairs of opposite sides are parallel TRAPEZOIDS Only one pair of Opposite sides parallel ISOSCLES TRAPEZOID A trapezoid that has two equal sides ROMBUS 4 equal sides RECTANGLE 4 right angles SQUARE Both a rhombus and a rectangle
8. 8. Properties of Parallelograms Diagonals are perpendicular to each other Diagonals bisect their angles Diagonals are congruent to each other Diagonals bisect each other Opposite sides are congruent Opposite angles are congruent Diagonals bisect each other Consecutive angles are supplementary Diagonals form two congruent triangles
9. 9. Area ½bh bh lw s 2 ½(b1 + b2 )
10. 10. Circles <ul><li>Exact: express in terms of π </li></ul><ul><li>Approximate: use an approximation of π (3.14) </li></ul>Circumference C = 2 π r or C = π d A = π r2
11. 11. Volume <ul><li>General Formula: V = (area of base)(height) </li></ul>e 3 π r 2 h π r 2 h lwh Bh π r 3