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BIO 100

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Lecture Geometry By the end of this lesson, students will be able to: 1. Differentiate between, describe and name lines, rays and line segments. 2. Identify and describe acute, right, obtuse, straight and reflex angles. 3. Find parallel and perpendicular lines to a line when given the equation for that line. 4. Define reflection symmetry. 5. Identify lines of reflection symmetry on various shapes. 6. Predict the two-dimensional shape created when taking the cross section of a three-dimensional object. 7. Find the area and volume of various objects.

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Lines, Rays and Segments In our everyday lives, if something is straight, we usually say that its in a line or is a line. However, in mathematics, a line has some specific requirements. Which of these is truly a line (mathematically)?

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Lines, Rays and Segments (Cont.) To understand lines, we should first understand what a point is. - A point represents a unique location in space, usually represented with coordinates, x and y. (We would also use a z coordinate if we were working in three dimensions.)

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Lines, Rays and Segments (Cont.) Point (x, y, z) Can you find the 3 planes?

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Lines, Rays and Segments (Cont.) To describe a line, mathematicians would say that a line is a series of points (infinite in both directions) that all lie on a single plane that make an infinitely small curve (meaning its straight). We name a line using any two points on the line. Name this line. A B C

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Lines, Rays and Segments (Cont.) To describe a ray, mathematicians would say that a ray is also an infinite series of points (like a line), but it has one endpoint and is only infinite in one direction. We name a ray by starting with its endpoint, then using any other point on the line. Name this ray. A B C

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Lines, Rays and Segments (Cont.) To describe a line segment, mathematicians would say that a line segment is a finite series of points, with two endpoints. (Rays and lines both have infinite length, but a line segment does not.) We name a line segment with its two endpoints. Name this line segment. A B C

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Angles An angle can be described as the amount of turn or the number of degrees between two intersecting lines, rays or line segments. Since the human body has many moving parts, a working knowledge of angles is important.

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Angles (Cont.) Well focus on six different types of angles.

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Acute Angles Acute can mean two different things in medicine. If you have acute pain, that means that your pain is sharp. Or, if you have a condition that is not long-lasting, that can also be referred to as acute. With these definitions in mind, we can see how an acute angle has an appropriate name. An acute angle is less than 90 degrees

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Right Angles and Obtuse Angles Right angles are exactly 90 degrees. It does not always mean turning right. An obtuse angle is greater than 90 degrees, but less than 180 degrees. An obtuse angle is in between 90 degrees and 180 degrees A right angle is exactly 90 degrees

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Straight Angles and Reflex Angles Straight angles are exactly 180 degrees. Two lines, rays or line segments meet to make a straight line. A reflex angle is greater than 180 degrees. A reflex angle goes beyond 180 degrees, a hyperextension A straight angle is exactly 180 degrees

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A Full Rotation When someone changes his/her mind, would you say that person did a 180 or a 360? Can you think of some parts of the body that can make these angles? A full rotation is 360 degrees

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Parallel and Perpendicular Lines Parallel and perpendicular lines are found on the same planelike a coordinate plane. Parallel lines have the same slope, while perpendicular lines meet at a right angle. Parallel lines Perpendicular lines

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Parallel Lines Find and name the two parallel lines. Then, find the equation for each one (in slope-intercept form).

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Parallel Lines (Cont.) The equation for line AB is... y = 2x + 1 The equation for line CD is... y = 2x 2 OR y = 2x + -2 What do you notice about these two equations? Give the equations for 5 other lines that are parallel to these lines. Graph a few.

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Perpendicular Lines Find and name the line that is perpendicular to Line AB. Then, find the equation for that line (in slope-intercept form).

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Perpendicular Lines (Cont.) The equation for line AB is... y = 2x + 1 The equation for line EF is... y = (-1/2)x + 3 What do you notice about these two equations (specifically, the slope)? Give the equations for 5 other lines that are perpendicular to line AB. Graph a few.

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Symmetry