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# Math 010: Chapter 9 Geometry Lines, figures, & triangles - PowerPoint PPT Presentation

Math 010: Chapter 9 Geometry Lines, 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

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

November 25, 2013

• 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

• 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

• 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 add up to 90˚

• Solve for x.

• (x+3)˚ + (2x – 3)˚ = 90˚

• x˚ +3˚ + 2x˚ – 3˚ = 90˚

• 3x˚ = 90˚

• x = 30˚

• 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˚

• 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 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!

• 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˚

• All angles in a triangle add up to 180˚

• Find C.

• 38˚ + 85˚ + C = 180˚

• 123˚ + C = 180˚

• C = 57˚

• 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

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

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

• 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 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

• 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”

• 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 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

• Same size and shape – the exact same triangle

• Rules to remember: ASA, SAS, SSS

• Be able to identify which rule applies

SAS

• 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).