Scale drawings
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This document discusses scale drawings and how they are used to represent real-life objects when drawing them is not possible at their actual size. It provides an example of a van that is 6 meters long being drawn at a scale of 1 centimeter to 20 centimeters, so that the drawing will fit on a single sheet of paper. It also gives an example of using a scale drawing and proportion to determine that if a vehicle's drawing is 30 cm long, then the actual vehicle is 600 cm or 6 meters long.
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The document discusses scales used in maps, models, plans and drawings. It explains that a scale is a ratio that compares the size of an object to its representation. It provides examples of different scales using ratios such as 1cm = 2cm at a scale of 1:2, 1cm = 3cm at a scale of 1:3, and 5cm = 1cm at a scale of 5:1. It concludes by instructing the reader to practice scaling images using the Keynote app on their device.
Scales
The document discusses scales used on engineering and architect scales and for measuring drawings. The 10 and 16 scales can be used as rulers. Scales are used to measure lines on drawings and reduce or enlarge drawings. If a drawing has a scale of 1/8" = 1', the architect scale should be used to measure. Examples show how to determine actual lengths from measured lengths on drawings using given scales.
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The document outlines a multi-part school project for students. They must:
1) Create a scale drawing of a 2 bedroom house with specific rooms and measurements.
2) Use the scale drawing to create a larger 3D model of the house, including furniture to scale in each room.
3) Complete a chart showing the scale calculations between the drawing, model, and real measurements.
Students must meet deadlines on February 1st, 28th, and 28th to receive credit which counts as two test grades.
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The document provides an introduction to map making. It defines what a map is, including definitions from sources like the International Cartographic Association. It discusses important historical maps created by Muslims. The document outlines the importance of maps and criteria for a good map. It describes different types of maps like reference maps, thematic maps, and components of maps such as titles, legends, scales, and directional indicators.
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2) To determine if two lines are parallel or perpendicular, you calculate their slopes. If the slopes are equal, the lines are parallel. If the slopes are negative reciprocals, the lines are perpendicular.
3) To find the equation of a line parallel or perpendicular to a given line, you use the slope of the given line and the point-slope formula. For a parallel line, you use the same slope. For a perpendicular line, you use the negative reciprocal slope.
5.2 bisectors of a triangle
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4.4 rates of change
This document contains examples of using graphs and tables to determine rates of change. Example 5 shows a table with time and cost for using an internet cafe, and calculates the rate of change in cost with respect to time as $3.50 per hour. Example 6 uses a graph to show attendance at a community theater over 10 weeks, finding different rates of change between weeks. Example 7 interprets a graph of distance over time to describe a student's commute of walking then waiting for the bus then riding the bus.
4.3 4.4 sas and asa proofs
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
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This document discusses different ways to prove triangles are congruent using congruence postulates. It introduces the Side-Side-Side (SSS) postulate, which states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent. It also introduces the Side-Angle-Side (SAS) postulate, which states that if two sides and the included angle of one triangle are congruent to those of another triangle, then the triangles are congruent. Examples are provided to demonstrate using each postulate to prove triangles congruent. The document asks readers to practice identifying which postulate could be used to prove triangles congruent in different scenarios.
4.1 triangles and angles
Triangles have three line segments that join three non-collinear points called vertices. Triangles are classified by their sides and angles. The Triangle Sum Theorem states that the sum of the interior angles of any triangle is 180 degrees. This is proved using parallel lines and angle addition. A corollary is that the acute angles of a right triangle are complementary to 90 degrees. The Exterior Angles Theorem states that an exterior angle is equal to the sum of the two non-adjacent interior angles. Examples show using these theorems to find missing angle measures.
Proving lines are perpendicular
This document discusses properties and theorems related to perpendicular lines:
- Two lines are perpendicular if the product of their slopes is -1. Vertical and horizontal lines are also perpendicular.
- If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.
- If two lines are each perpendicular to the same line, then they are parallel to each other.
- It provides a proof that if two coplanar lines are each perpendicular to the same line, then they are parallel to each other.
- Examples are given to determine if given lines are perpendicular or parallel based on their slopes or equations. Homework exercises are assigned from the textbook.
3.2 theorems about perpendicular lines
The document discusses different types of proofs used to prove theorems about perpendicular lines. It presents three theorems: 1) if two lines intersect to form congruent angles, they are perpendicular, 2) if two adjacent acute angles have perpendicular sides, they are complementary, and 3) if two lines are perpendicular, they intersect to form four right angles. It also provides an example proof of theorem 3.2 using a two-column format.
Proving lines are parallel
The document discusses several theorems and properties for proving when two lines are parallel, including:
1) If corresponding angles formed by a transversal intersecting two lines are congruent, then the lines are parallel.
2) If alternate interior angles or alternate exterior angles formed by a transversal are congruent, then the lines are parallel.
3) If consecutive interior angles formed by a transversal are supplementary, then the lines are parallel.
It also provides an example of using these properties to prove that if two boats sail at 45 degree angles to the constant wind, their paths will not cross since their paths are parallel.
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A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptx
Your Skill Boost Masterclass: Strategies for Effective Upskilling
Your Skill Boost Masterclass: Strategies for Effective Upskilling