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Study Notes Geometry

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Symmetry You will need to know how to complete a congruent side of a picture To do this, you may choose from one of the following Use grid paper Use a transparent mirror Trace original side at a window or on a computer screen When you are drawing the congruent half, measure the distance of a point to the line of symmetry at right angles and produce a matching point on the other side of the line – find at least three matching points to draw Go to this link for more practice: Lesson 1

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**Constructing Triangles**

You need to know how to draw triangles when given angle measures and side lengths Use a protractor and a ruler (your measurement needs to be within 2 degrees Make sure your pencil is sharp Know that when one side and one angle are given, there are infinite number of triangles that can be drawn Always label side lengths showing units Always label angles

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**Construct the following**

One side length is 7cm and one angle is 80 degrees One side length is 7cm and two angles are 80 degrees and 60 degrees Two side lengths are 5cm each and the angle between them is 105 degrees Practice on the following link: Lesson 2

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**Classifying Triangles by Angles**

Triangles can be named by looking at the angles and estimating right, obtuse or acute Any triangle with a 90 degree angle is called a Right-Angled Triangle Any triangle with one obtuse angle (over 90 degrees) is called an Obtuse-Angled Triangle All angles must be acute angles to be called an Acute-Angled Triangle (think tiny and cute) Some people just look for the largest angle of any triangle and classify (name it) based on that angle Be sure to know how to order different polygons from greatest to least angle size Lesson 3

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**Classifying Triangles by Side Lengths**

Triangles can be named by looking at the side lengths A triangle with three equal side lengths is called an Equilateral Triangle (think of equal) A triangle with two equal side lengths is called an Isosceles Triangle (think of two eyes) A triangle with three different side lengths is called a Scalene Triangle

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**Classifying Triangles by Side Lengths cont….**

Know that an Equilateral Triangle has three lines of symmetry Know that an Isosceles Triangle has one line of symmetry Know that a Scalene Triangle has no lines of symmetry Lesson 4

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**Measuring Angles in Polygons**

Regular Polygons are shapes that have equal side lengths and equal angles

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**Measuring Angles in Polygons cont…**

Regular Polygons As the number of sides increases, so does the angle size increase 3-sided regular polygon is a triangle 4-sided regular polygon is a square 5-sided regular polygon is a pentagon 6-sided regular polygon is a hexagon (x) 8-sided regular polygon is an octagon

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**Measuring Angles in Polygons cont…**

Irregular Polygons have different length sides and different size angles Lesson 5

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**Properties of Polygons**

Know that polygons can be described using the following properties Number of sides and angles Side lengths Angle measures Number of parallel sides Number of lines of symmetry Ticks show different side lengths Arrows show parallel sides Polygons have a fixed set of properties which do not change when the size or orientation is changed When a shape is enlarged or shrunken, or moved to a different place, the angle measures stay the same, and the parallel sides and lines of symmetry do not change Lesson 6

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Sorting Polygons You will need to identify the properties of the polygons in a Venn Diagram You will be given a different property for each circle and polygons that have both of those properties go in the middle overlap Polygons or circles that do not have either of the two properties, go outside of the Venn Diagram Lesson 7

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**Sorting Polygons cont…**

When sorting polygons, any of the following may be asked for: Number of sides Number of angles Side lengths Angle measures Number of parallel sides Number of lines of symmetry Regular vs irregular polygons

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**Communicating about Shapes**

You will need to be able to describe thoroughly the properties of polygons so that I would be able to draw the shape from your description You need to use vocabulary from the list provided in the slide before Lesson 8

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**More websites to visit Mathfrog.ca Mathies.ca Khan Academy**

Study a little every night to assure you have a complete understanding of the concepts!

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