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Geometry

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Conic Sections

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THIS IS All With... 100 100 100 100 100 100 200 200 200 200 200 200 300 300 300 300 300 300 400 400 400 400 400 400 500 500 500 500 500 500 Who Am I? Terms Graph & Label Write equations Solving Hodge Podge 3x2 + 3y2 = 3 A 100 Circle A 100 5x2 + 6y2 + 5x ? y = 11 A 200 Ellipse A 200 2x2 + 7x + + 5y = y2 + 9 A 300 Hyperbola A 300 3x + 4y2 + 5x + 11y = 18 A 400 Parabola A 400 Eccenticity = .87 A 500 Ellipse A 500 B 100 Minor Axis B 100 B 200 B 200 Foci B 300 Co-vertices B 300 B 400 Conjugate Axis B 400 Name the 2 lines below. B 500 Horizontal: Directrix Vertical: Axis of symmetry B 500 x2 + y2 + -10x +8y +5 = 0 C 100 (x ? 5)2 + (y + 4)2 = 36 C 100 x2 + 4y2 + 10x + 24y + 45 = 0 C 200 (x + 5)2 + (y +3)2 = 1

Geometry Things to Remember

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Copyright ? Regents Exam Prep Center Geometry ? Things to Remember! Regular Solids: Tetrahedron ? 4 faces Cube ? 6 faces Octahedron ? 8 faces Dodecahedron ? 12 faces Icosahedron ? 20 faces 3-D Figures: Prism: V = Bh Pyramid: 1 3 V Bh= Cylinder: 2V r h?= ; 22 2SA rh r? ?= + Cone: 2 1 3 V r h?= ; 2SA s r r? ?= + Sphere: 3 4 3 V r?= ; 2 24SA r d? ?= = Locus Theorems: Fixed distance from point. Fixed distance from a line. Equidistant from 2 points. Equidistant 2 parallel lines. Equidistant from 2 intersecting lines Polygon Interior/Exterior Angles: Sum of int. angles = 180( 2)n ? Each int. angle (regular) = 180( 2)n n ?

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Proving triangles similar

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Honors Geometry Lesson 8.5 Proving that Triangles are Similar What You Should Learn Why You Should Learn It How to use the SSS and SAS Similarity Theorems to prove that two triangles are similar How to use similar triangles to solve real-life problems You can use similar triangles to solve real-life problems such as understanding how a pantograph can be used to enlarge a figure Ways to Prove that Triangles are Similar Definition of similar triangles AA Similarity Postulate Side-Side-Side (SSS) Similarity Theorem Side-Angle-Side (SAS) Similarity Theorem Theorem 8.2 Side-Side-Side (SSS) Similarity Theorem If corresponding sides of two triangles are proportional, then the two triangles are similar Proof of SSS Similarity Theorem S T R M L N P Q

Naming defintions of theorems, or postulate NOTES

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1. two anglesthat are supplementary add up to 180 - def. of supplementary angles 2. If two angles of obne trianlge are equal to two angles of another triangle, then the third angles are equal. -AA(angle angle) 3.Two angles that form a linear pair add up to 180 -linear pair postulate 4. The sum of the measure of the interior angles of a triangle is 180 -triangle sum theorm

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