Math 010: Chapter 9 Geometry Lines, figures, &amp; triangles

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Math 010: Chapter 9 Geometry Lines, figures, &amp; triangles. November 25, 2013. 9.1 Intro to Geometry (Lines &amp; Angles). Lines have infinite length, they go on forever Line segments have a finite length The length of a segment is denoted by the two endpoints. AB = distance between A and B

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### Math 010: Chapter 9GeometryLines, figures, & triangles

November 25, 2013

9.1 Intro to Geometry (Lines & Angles)
• Lines have infinite length, they go on forever
• Line segments have a finite length
• The length of a segment is denoted by the two endpoints. AB = distance between A and B
• AD = length of the whole line segment
Know how to construct & solve this equation
• If AD = 12 cm, AB = 5 cm, and CD = 4 cm, find the length of BC.
• 5cm x 4cm
• 5 + x + 4 = 12
• x + 9 = 12
• x = 3
• Final Answer: BC = 3 cm
Solve a supplementary angles equation
• 180˚ is a straight line
• Supplementary angles add up to 180˚
• Think straight = supplementary
• What is the value of b?
• 45˚ +39˚ + b + 24˚ = 180˚
• b + 108 = 180
• b = 72˚
Complementary angles equation
• Complementary angles add up to 90˚
• Solve for x.
• (x+3)˚ + (2x – 3)˚ = 90˚
• x˚ +3˚ + 2x˚ – 3˚ = 90˚
• 3x˚ = 90˚
• x = 30˚
Angles: Types of angles
• 1. Acute angles are smaller than 90 degrees
• Examples: 10˚, 45˚, 80˚
• 2. Rightangles are 90 degrees
• Perpendicular lines are lines that form a right angle
• 3. Obtuse angles are larger than 90 degrees and smaller than 180 degrees
• Examples: 100˚, 160˚, 95˚
Vertical angles are congruent
• Congruent angles have equal measure.
• Vertical angles are the angles formed across from each other by two intersecting lines.
• Also note that 134˚ and 46˚ are supplementary
Parallel lines and transversals
• Parallel lines are lines that will never intersect no matter how long you draw them.
• A transversal is a line that intersects two other lines at different points
• Alternate interior angles are shown here:
• AIA’s are congruent!
Know how to fill in all angle measures
• Given: <1 measures 110˚
• Note that <1 and <2 are supplementary
• So <2 measures 70˚
• All angles in this picture measure either 110˚ or 70˚
Triangle equation
• All angles in a triangle add up to 180˚
• Find C.
• 38˚ + 85˚ + C = 180˚
• 123˚ + C = 180˚
• C = 57˚
9.2 Plane Geometric Figures
• Polygons are shapes made up of 3 or more line segments: triangles, rectangles, octagons, etc.
• Circles, ovals are not polygons.
• A regular polygon is a polygon where all sides are equal, and all angles are equal.
• Know this: a pentagon has 5 sides. A hexagon has 6 sides.

hexagon

pentagon

Types of triangles
• Know what an isosceles, equilateral, scalene, and right triangle are.

A right triangle has one right (90˚) angle.

Perimeter
• The perimeteris the distance around the outside of a figure.
• To find the perimeter of a polygon, add up all the side lengths.
• Perimeter of this rectangle

= 2 cm + 6 cm + 2 cm + 6 cm = 16 cm

Circumference
• Circumference is the distance around a circle.
• C = 2πr or πd
• Find the circumference of a circle with diameter 10.
• Circumference = 10π
• Find the circumference of a circle with radius 2.
• Circumference = 2π2 = 4π
Area of a circle
• First need to square r (order of operations)
• Find the area of a circle with radius 5.
• 5 squared is 25
• A = 25π
• Remember the two circle formulas
• Area is the one containing “squared”
9.3 Triangles
• The hypotenuse of a right triangle is the side opposite the right angle.
• Pythagorean Theorem: where c is the hypotenuse.
• Use this theorem with the “3-4-5” triangle
• On exam, show this process to find the value of the hypotenuse.
Similar triangles
• Similar means same shape
• Does not mean same size
• Angle measures same
• Side lengths proportional
• Know how to find missing side
• Multiplication
• We know 14 = 7 · 2;
• 12 = 6· 2
• So, 10 · 2 = 20
Congruent triangles
• Same size and shape – the exact same triangle
• Rules to remember: ASA, SAS, SSS
• Be able to identify which rule applies

SAS

Quiz
• Overall, rate how confident you feel (1-5, 5 best) about the following:
• Geometry vocab
• Lines and angles equations
• Area formulas
• Similar triangles (proportion)
• Congruent triangles rules
• If <1 = 60˚, find the measures of all other angles (2 through 8).