geometry
TRANSCRIPT
Geometry
AnglesParallel LinesTrianglesQuadrilaterials– ParallelogramsAreaCirclesVolume
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 23 4
5 67 8
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 23 4
5 67 8
Supplementary Angle Pairs formed by
Parallel Lines
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:
Two sides are equal One
Right angle
All sides are equal
Scalene Isosceles Equilateral Right
No sides are equal
QUADRILATERALS
PARALLELOGRAM
Both pairs of opposite sides are parallel
TRAPEZOIDS
Only one pair of Opposite sides parallel
ISOSCLESTRAPEZOID
A trapezoid that hastwo equal sides
ROMBUS4 equal sides
RECTANGLE
4 right angles
SQUARE
Both a rhombusand a rectangle
Properties of Parallelograms
Diagonals are perpendicular to each other
Diagonals bisect their angles
Diagonals are congruent to each other
Diagonals bisect each otherOpposite sides are congruentOpposite angles are congruentDiagonals bisect each otherConsecutive angles are supplementaryDiagonals form two congruent triangles
Area
½bh bh
lw
s2
½(b1 + b2 )
Circles
• Exact: express in terms of π• Approximate: use an approximation of π (3.14)
Circumference
C = 2πr or C = πd
A = πr2
Volume
General Formula: V = (area of base)(height)
3
1
3
1
e3
πr2hπr2hlwh
Bh
3
4πr3