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Euclidean geometry

Geometry TN 2018 2019 Curriculum Map Q1

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Geometry
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Curriculum and Instruction ? Mathematics Quarter 1 Geometry Mathematics Geometry: Year at a Glance 2018 - 2019 Aug. 6 ? Oct. 5 Oct. 16 - Dec. 19 Jan. 7 ? Mar. 8 Mar. 18 ? May 24 TN Ready Testing Apr. 22 - May23 Tools of Geometry, Reasoning and Proof, Transformations and Congruence, Transformations and Symmetry, Lines and Angles Triangle Congruence with Applications, Properties of Triangles, Special Segments in Triangles, Properties of Quadrilaterals with Coordinate Proofs Similarity and Transformations, Using Similar Triangles, Trigonometry with Right Triangles, Trigonometry with All

Geometry notes

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Lesson 3.03 KEY Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE or DRAWING Objective After completing this lesson, I will be able to: construct congruent triangles explain why the constructed triangles are congruent Constructing Congruent Triangles (P1-2) Congruent triangles may be constructed by hand using a COMPASS and STRAIGHTEDGE. Congruent triangle may also be constructed using computer technology such as GEOGEBRA. Constructing Congruent Triangles based on S-S-S Postulate (P3) ?ABC is congruent to ?DEF because segment f was constructed with the same length as segment b. Segment e was constructed with the same length as segment c, and segment d was constructed with the same length as segment a. By the SIDE-SIDE-SIDE postulate, ?ABC ?DEF.

Geometry Theorems and Postulates

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MATH NOTES PART ONE Geometry- A metric system of measuring the earth Four parts of a mathematics system- undefined terms, defined terms, postulates, theorems Defined terms- postulates, theorems Undefined terms- a point (use capitals), a line (name it with capitals, or name it line l), a plane (adds a new dimension) Zero-dimension- the dimension of a point One-dimension- the dimension of a line Two-dimensional- the dimension of a plane Collinear- when two points are on the same line Non-collinear- when two points are NOT on the same line Non-coplanar- if the point can never be in the plane Postulates- statements accepted without proof Theorem- statements that can be proven with postulates Segment- is part of a line that has two endpoints

Triangles

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Geometry
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There are 3 types of triangles including isosceles, scalene,and equilateral triangles. Triangles can be obtuse, acute, or right triangles. Some special measurements of a triangle are 30-60-90 and 45-45-90 triangles. Different ways can be used to find missing side lengths and angle measurements.

Geometry

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Geometry
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Geometry Notes ~Reflectional Symmetry -When a shape is folded in half and both sides match perfectly. ~Line of Symmetry -line where you can fold it ~Perimeter -the distance around its exterior on a flat surface. ~Area -the number of square units needed to fill up a region on a flat surface. ~Acute Angle -Any angle with a measure between 0 degrees and 90 degrees ~Right Angle -Any angle that measures 90 degrees ~Obtuse Angle -Any angle with a measure between 90 degrees and 180 degrees ~Straight Angle -Angle that has a measure of 180 degrees and are formed when the sides of an angle form a straight line. ~Transformation 1) Translation: A transformation that?s shape and size stays the same while sliding it to a new location.

Geometry

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Geometry
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Geometry Notes ~Reflectional Symmetry -When a shape is folded in half and both sides match perfectly. ~Line of Symmetry -line where you can fold it ~Perimeter -the distance around its exterior on a flat surface. ~Area -the number of square units needed to fill up a region on a flat surface. ~Acute Angle -Any angle with a measure between 0 degrees and 90 degrees ~Right Angle -Any angle that measures 90 degrees ~Obtuse Angle -Any angle with a measure between 90 degrees and 180 degrees ~Straight Angle -Angle that has a measure of 180 degrees and are formed when the sides of an angle form a straight line. ~Transformation 1) Translation: A transformation that?s shape and size stays the same while sliding it to a new location.

Why triangles are equilateral!

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Because they are triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. A triangle with vertices A, B, and C is denoted ABC. In Euclidean geometry any three non-collinear points determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space).

Pythagorean Theorem

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This formula is extremely essential especially later on. Note that this formula only applies to right triangles.  The formula is

a^2+b^2=c^2

A and B being the two legs.

C being the hypotenuse of the triangle.

The hypotenuse (c) is the side opposite the largest angle in the triangle.  In this case for a right triangle, the hypotenuse will always be opposite of the right angle.

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