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Elementary geometry

Geometry TN 2018 2019 Curriculum Map Q1

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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.

math study guide 4 grade

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Math study guide Discrete a point is a dot T geometry a line is a set of dots in a row T a line has no thickness F 2 crossing lines intersect in a point F Synthetic a point is a physical dot F (exact location) Geometry a line is a set of points going in both directions going the shortest paths T A line has no thickness T A line extends 2 directions T Plane coordinate a point is an ordered pair of numbers not a # T Geometry a line is a set of ordered pairs that go with ax+by=c when they are both not 0 T

Geometry Theorems and Postulates for a Midterm

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DEFINITIONS?Def. line segment (segment) - part of a line that has 2 definite endpoints?Def. ray - part of a line that starts with a definite endpoint and extends indefinitely in 1 direction?Def. angle - the union of 2 noncollinear rays with a common endpoint?Def. union - elements belonging in 1 or both sets?Def. intersection - elements that belong to both sets?Def. absolute value - |x| = if x _>_ 0; -x if x _<_ segment="" length="" the="" distance="" between="" endpoints="" congruent="" segments="" with="" same="" midpoint="" a="" point="" b="" is="" called="" of="" lineac="" if="" c="" and="" ab="BC?Def." bisector="" line="" ray="" or="" plane="" that="" passes="" through="">

Geometry for Enjoyment and Challenge Notes 5.3

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Congruent Angles in Parallel Lines Alternate interior angles congruent -> Parallel lines yields alternate interior angles congruent Alternate exterior angles congruent -> Parallel lines yields alternate exterior angles congruent Corresponding angles -> Parallel lines yields corresponding angles congruent Consecutive interior angles supplementary -> Parallel lines yields consecutive interior supplementary Consecutive exterior angles supplementary -> Parallel lines yields consecutive exterior supplementary Ex. 1 ________________/__________________ Solve for X / 3x + 5 / / 2x + 10 / _____________/_____________________ Answer: 3x+5=2x+10 => x=5

Geometry for Enjoyment and Challenge Notes 5.3

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Congruent Angles in Parallel Lines Alternate interior angles congruent -> Parallel lines yields alternate interior angles congruent Alternate exterior angles congruent -> Parallel lines yields alternate exterior angles congruent Corresponding angles -> Parallel lines yields corresponding angles congruent Consecutive interior angles supplementary -> Parallel lines yields consecutive interior supplementary Consecutive exterior angles supplementary -> Parallel lines yields consecutive exterior supplementary Ex. 1 ________________/__________________ Solve for X / 3x + 5 / / 2x + 10 / _____________/_____________________ Answer: 3x+5=2x+10 => x=5

Stuff

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Theorem Hypothesis Conclusion Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 4 3 1 2 1 ? 8 7 6 5 P Q ?1 ? ?3 ?2 ? ?4 ?5 ? ?7 ?6 ? ?8 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 22 1 4 3 ?1 ? ?3 ?2 ? ?4 Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of alternate exterior angles are congruent. 5 6 8 7 ?5 ? ?7 ?6 ? ?8 Same-Side Interior Angles Theorem If two parallel lines are cut by a transversal, then the two pairs of same side interior angles are supplementary. 4 1 2 3

Algebra Sin, Cos, and Tan

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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:

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