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Triangle geometry

Geometry TN 2018 2019 Curriculum Map Q1

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Geometry
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Equivalence
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Perpendicular
Congruence
Transversal
Angle

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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Triangle

Lesson 3.02 KEY Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE or DRAWING Objective After completing this lesson, I will be able to __________________________________________ Proving Congruency (P2) To prove congruency in two triangles you need _____________________, or parts that match up with one another; the parts have to match up, and ____________ of the parts matters. CORRESPONDING Parts (P3) The CORRESPONDING parts are the ones that match up with one another. THREE Congruent Parts (P4) Triangles must have at least THREE congruent parts for them to be considered CONGRUENT SSS (P5) Side?Side?Side Postulate If all three sides are congruent to all three sides of another triangle, then the two triangles are CONGRUENT SAS (P7)

Geometry notes

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Triangles

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.

Triangle Properties

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Dimension
Triangle properties Vertex The vertex (plural: vertices) is a corner of the triangle. Every triangle has three vertices. Base The base of a triangle can be any one of the three sides, usually the one drawn at the bottom. You can pick any side you like to be the base. Commonly used as a reference side for calculating the area of the triangle. In an isosceles triangle, the base is usually taken to be the unequal side. Altitude The altitude of a triangle is the perpendicular from the base to the opposite vertex. (The base may need to be extended). Since there are three possible bases, there are also three possible altitudes. The three altitudes intersect at a single point, called the orthocenter of the triangle. See Orthocenter of a Triangle.

Algebra Sin, Cos, and Tan

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Right triangle
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Sine
Right angle
Adjacent
A right-angled triangle is a triangle in which one of the angles is a right-angle. The hypotenuse of a right angled triangle is the longest side, which is the one opposite the right angle. The adjacent side is the side which is between the angle in question and the right angle. The opposite side is opposite the angle in question. In any right angled triangle, for any angle: The sine of the angle = the length of the opposite side the length of the hypotenuse The cosine of the angle = the length of the adjacent side the length of the hypotenuse The tangent of the angle = the length of the opposite side the length of the adjacent side So in shorthand notation:

Triangles

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Special right triangles
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.

Sin Cos and Tan

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Sin Cos Tan
In a right triangle where theta is given and a side is given you can solve for anything. To solve for the hypotenuse use the phrase SOH CAH TOA. If the angle and the opposite are given use opposite side divided by sin of the angle. and vice versa for all other sides and angles. Soh cah toa stands for Sin opposite over Hypotenuse Cosin adjacent over hypotenuse Toa opposite over adjacent all of these are with respect to theta.

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).

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