Drawing triangles
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This document provides instructions for drawing different types of triangles based on given information: 1. When given one angle and the lengths of two sides, use a protractor and ruler to draw the triangle. 2. When given the measures of two angles and the length of one side, construct the triangle using a protractor and ruler. 3. When given the lengths of all three sides but no angles, use a compass and ruler to draw the triangle.
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Let's solve this step-by-step:
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Triangle ppt
This document provides an overview of triangles, including definitions, types, properties, secondary parts, congruency, and area calculations. It defines a triangle as a 3-sided polygon with three angles and vertices. Triangles are classified by side lengths as equilateral, isosceles, or scalene, and by angle measures as acute, obtuse, or right. Key properties discussed include the angle sum theorem, exterior angle theorem, and Pythagorean theorem. Secondary parts like medians, altitudes, perpendicular bisectors, and angle bisectors are also defined. Tests for triangle congruency such as SSS, SAS, ASA, and RHS are outlined. Formulas are provided for calculating the areas of
Triangle and its properties
This document discusses several key properties of triangles. It states that the sum of the interior angles in any triangle is always 180 degrees, known as the angle sum property. It also notes that an exterior angle is equal to the sum of the opposite interior angles. Additionally, the document explains that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, known as the Pythagorean theorem.
Triangles
This document discusses various theorems and properties related to triangles. It explains the Basic Proportionality Theorem, also known as Thales' Theorem, which states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. It also covers similarity criteria like AAA, SSA, and SSS. The Area Theorem demonstrates that the ratio of areas of similar triangles equals the square of the ratio of corresponding sides. Additionally, it proves Pythagoras' Theorem, which relates the sides of a right triangle, and its converse. In summary, the document outlines key triangle theorems regarding proportional division, similarity, areas, and the Pythagorean relationship between sides.
Triangles
Triangles are three-sided polygons that have three angles and three sides. There are three main types of triangles based on side lengths: equilateral (all sides equal), isosceles (two sides equal), and scalene (no sides equal). The interior angles of any triangle always sum to 180 degrees. Important triangle properties include the exterior angle theorem, Pythagorean theorem, and congruency criteria like SSS, SAS, ASA. Common secondary parts are the median, altitude, angle bisector, and perpendicular bisector. The area of triangles can be found using Heron's formula or other formulas based on side lengths and types of triangles.
Constructing an angle or triangle using a protractor
This document provides instructions for constructing angles and triangles using a protractor, ruler, and pencil given specific measurements. For angles, the steps are to rule a horizontal line, place the protractor at one end with the center, mark the desired degree at the edge, and rule a line from the end of the first line to the mark. For triangles, the steps are to rule lines for the two given side lengths, place the protractor at an end to mark the angle degree, rule the third side to complete the triangle, and label all measurements. Practice exercises are provided to construct various angles and triangles.
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Pascal’s triangle and its applications and properties
Pascal’s triangle and its applications and properties
Angle Pairs (Complementary, Supplementary, Adjacent, Vertical, Linear Pair)
Angle Pairs (Complementary, Supplementary, Adjacent, Vertical, Linear Pair)
Constructing an angle or triangle using a protractor
Constructing an angle or triangle using a protractor
More from Terry Golden
Scatter graphs
The document discusses scatter diagrams and their use in showing the relationship between two variables. Scatter diagrams involve plotting paired data points for each variable on a graph, allowing one to see if there is a correlation between the variables. Examples are provided of scatter diagrams plotting ice cream sales against hours of sunshine and city temperature against latitude. Scatter diagrams can reveal trends and relationships in data.
Reflections rotations translations
1. The document discusses different types of geometric transformations including reflections, rotations, and translations.
2. A reflection produces a mirror image of an object across a line or plane. Corresponding points on the object and its reflection are equidistant from the line/plane of reflection.
3. A rotation turns an object around a fixed point by a specified angle and direction. To perform a rotation, one traces the object onto tracing paper and rotates the paper around the given point by the required angle and direction.
Ratio
The document discusses ratios and provides examples of how to use ratios to solve problems. Ratios compare the relative amounts or proportions of different parts of a quantity. Examples show how to set up and solve ratio problems involving splitting costs or quantities between groups using the ratio and multiplying components by the same factor to keep the ratios equivalent.
Ratio share a quantity
The document discusses ratios and provides examples of how to use ratios to calculate quantities. It explains that a ratio shows a relationship between quantities and can be used to scale up or down amounts. Examples include baking a cake according to ingredient ratios and calculating the number of ducks in a pond given the ratio of geese to ducks. It also demonstrates how to scale recipe amounts for different numbers of people using ratios.
Probability not happening
1. The document discusses probability and provides examples of calculating the probability of events occurring and not occurring. It defines probability as being expressed on a scale of 0 to 1 or 0% to 100% and explains that the probability of an event not happening is 1 minus the probability of the event happening.
2. Examples are given of calculating probabilities using a die, deck of cards, weather forecast, and Mikel's transportation to school. The document concludes with an explanation of how to calculate the probability of an event not occurring by subtracting its probability from 1.
3. In summary, the document outlines basic probability concepts and provides examples of calculating probabilities of outcomes both occurring and not occurring using fractions, decimals, and
Probability exclusive
The document discusses mutually exclusive outcomes and probability. It provides examples of tossing a coin, where the outcomes of heads and tails are mutually exclusive and must add up to 1. It also gives an example of drawing balls from a bag containing red, blue and green balls, where the probabilities of drawing red and blue balls add up to 12/14, making the probability of drawing a green ball 2/14 or 1/7.
Powers
This document provides an explanation of powers and indices. It discusses how indices can be used to represent repeated multiplication, such as 22 representing 2 x 2 and 23 representing 2 x 2 x 2. It also explains that indices can be used in combination with each other and other mathematical functions. The document provides examples of calculating values of formulas when given specific values for variables. It notes that indices only apply to the previous number and brackets can be used to keep workings clear. Values substituted can be positive, negative, decimals or fractions.
Percentages
This document explains how to convert fractions to percentages in 3 main steps:
1) Convert the fraction to a decimal by dividing the numerator by the denominator. Then multiply the decimal by 100 to get the percentage.
2) Think of 100 as the denominator of an equivalent fraction. Find the equivalent fraction by setting 100 as the denominator.
3) Directly convert the fraction to a percentage by multiplying the fraction by 100 and simplifying. This skips converting to a decimal first.
Worked examples are provided to demonstrate both converting through decimals and directly to percentages.
Percentages one of another
This document discusses how to express one quantity as a percentage of another. It provides examples of calculating percentages, including percentage increases and decreases. It explains that a percentage of a number can be found by converting the percentage to a fraction or decimal and multiplying. The document also introduces methods to shorten the process of adding or subtracting percentages using multipliers.
Negative numbers multiplying and dividing
The document discusses multiplying and dividing decimals. It explains that when multiplying decimals, you ignore the decimal points, multiply the numbers, and count the total number of decimal places in the original numbers to determine where to place the decimal point in the answer. When dividing decimals, you write the division as a fraction and multiply the numerator and denominator by powers of ten to clear the decimals, then divide as usual. Examples of multiplying and dividing decimals are provided.
Negative numbers adding and subtracting
1. The document discusses adding and subtracting negative numbers using examples with biscuits. It explains that subtracting a negative number is the same as adding a positive number, and vice versa.
2. Quick rules are provided for subtracting or adding to negative numbers. When subtracting from a negative number, add the numbers and place a minus sign in front of the answer. When adding to a negative number, subtract the numbers and use the same sign as the larger number.
3. A method is described for calculating a string of additions and subtractions by separating the numbers into "add" and "subtract" totals and finding the difference between the totals.
Grouping data stem and leaf diagrams
This document explains how to represent math test score data for 30 students using a stem and leaf diagram. [1] The test scores ranged from 40 to 81 and are grouped into the 40s, 50s, 60s, 70s, and 80s. [2] The stem represents the tens place value and the leaves are the units that follow each ten. [3] The modal score is in the 60-69 group and the median score is 63.
Grouping data discrete
This document discusses grouping discrete data and calculating statistics like the mode, mean, and frequency. It provides an example of grouping the number of goals scored in soccer matches to find the mode of 3 goals. Another example calculates the mean shoe size from a survey by tallying shoe sizes into a frequency table and dividing the total by the number of participants.
Grouping data continuous
This document discusses representing and summarizing continuous data. Continuous data does not fit into categories but changes gradually, like height, weight, or temperature. When measuring continuous data, measurements are rounded and grouped at the level of accuracy used. Continuous data can be grouped into intervals and displayed using histograms or frequency polygons. The mean of grouped continuous data can be estimated using the midpoint of each interval multiplied by its frequency and dividing the total by the total frequencies.
Graphs 3
This graph shows Joe's trip to the local shop over time. It shows that Joe walked at a steady pace as the distance from his home to the shop increased linearly over 15 minutes. Then the distance remained the same as he spent more time at the shop before returning home. The graph uses distance from home on the y-axis and time on the x-axis to tell the story of Joe's shopping trip.
Graphs 2
This document discusses linear equations in the form of Ax + By = C and provides an example of solving for x and y when the other variable is 0. It shows setting 4x + 3y = 12 equal to 12 when x is 0, solving for y = 4, and when y is 0, solving for x = 3. These points (0,4) and (3,0) are plotted and joined with a straight line, and a point on the line is checked.
Graphs 1
The document discusses linear graphs and their properties. It explains that a linear graph can be represented by an equation in the form of y = mx + c, where m is the slope and c is the y-intercept. The document provides examples of drawing linear graphs from equations and calculating points to plot based on given x-values. Key aspects covered include the four quadrants of the Cartesian plane, common linear equations like y=3 and x=1, and plotting example graphs for equations like y=-2x+2.
Fractions multiplicatin
To multiply fractions:
1) Multiply the numerators together to get the new numerator
2) Multiply the denominators together to get the new denominator
3) Simplify the resulting fraction if possible by cancelling common factors in the numerator and denominator.
Fractions division
The document discusses dividing fractions. It explains that dividing by a fraction is the same as multiplying by its reciprocal. Specifically, it states that to divide fractions, you turn the second fraction upside down and change the division sign to a multiplication sign. This works for dividing any fractions. Two examples are provided to demonstrate dividing fractions using this method.
Factorising
This document discusses factorizing expressions. It provides examples of factorizing terms with variables like 8a - 4a = 4(2a - 1) and expressions with squared terms like 15x + 9^2 = 3(5x + 3^2). It concludes with practice problems factorizing additional expressions like 10x + 5 = 5(2x + 1) and their factorized forms.
More from Terry Golden (20)
Drawing triangles
- 1. October 4, 2012 Drawing triangles and other shapes 1. Drawing triangles Next
- 2. Explanation October 4, 2012 Sometimes you are asked to make an C 20cm accurate drawing of a sketch such as this… 40º You need a pencil, a protractor and a ruler. A 15cm B The anglepointanglepoint Bthefrom youryourthrough lies Usingthe 40º40º is mark thethis line40º angle, it point C. Mark and label20cmand lineusing pointto this as it the Label the ofjoining called to C, at and A, ruler. included label Draw a line ruler, drawto a , line using ruler. line. a protractor, Aalong point AC. your line a between40º. two lines of which you know the length. point at the C 20cm 40º A 15cm B More Next
- 3. Explanation October 4, 2012 Sometimes you are given one side and two R angles, like this… 35º 28º Again you need a pencil, a protractor P 12cm Q and a ruler. Measure the angle than PQ. The completed triangle.at Q. Draw andline QR. 28º PQ. the label the line a line longer 35º P. R 35º 28º P 12 cm Q More Next
- 4. Explanation October 4, 2012 You may be given the length of three sides, but no angles. Construct a triangle ABC with AB = 14 cm, AC 9 cm and BC = 13 cm. This time you will need a pencil, a ruler and a pair of compasses. C m1 9 c 3 cm A 14 cm B More Next
- 5. Explanation October 4, 2012 You may be given two sides and a non-included Z angle. That is an angle not between the two 10cm known sides. 60º The completedcrosses XY.cm Where to the with radiusfrom X. is Z. Measure arclonger thanthe line from Y. Join Ythe lineangle Draw an Z.arcXY. 60º 10 a the line triangle. X 8.6cm Y Z 10 cm 10 mc 60º X 8.6 cm Y More Next End