The Bronx Science Geometry Teachers Proudly Present… THE (ULTIMATE) GEOMETRY REVIEW SHEET (2012 Edition) Some General Information The Regents Exam Basics: Time: 3 hours Problems: 38 ● Part I: 28 multiple choice problems (2 pts each) = 56 pts ● Part II: 6 short answer problems (2 pts each) = 12 pts ● Part III: 3 short answer problems (4 pts each) = 12 pts ● Part IV: 1 long answer problem (6 pts each) = 6 pts ● Total: 86 pts
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(X2-X1)2+(Y2-Y1)2 Angle-consists of 2 diff rays that have the same initial angle Sides-(rays) sides of an angle Vertex-initial part of an angle Congruent angles- angles w/ the same measure. Adjacent angle- angles that share a common vertex and side but have no common interior points Midpoint- the point that divides or Bisects-the segment into 2 congruent segments Segment Bisector- segment‚ ray‚ line‚ plane that intersects a segment at its midpoint MIDPONT FORMULA
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Right Angles All right angles are congruent. Straight Angles All straight angles are congruent. Congruent Supplements Supplements of the same angle‚ or congruent angles‚ are congruent. Congruent Complements Complements of the same angle‚ or congruent angles‚ are congruent. Linear Pair If two angles form a linear pair‚ they are supplementary. Vertical Angles Vertical angles are congruent. Triangle Sum The sum of the interior angles of a triangle is 180º. Exterior Angle The
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Activity Lesson for specific directions** Step 1: Translations and SSS Identify and label three points on the coordinate plane that are a translation of the original triangle. Next‚ use the coordinates of your translation along with the distance formula to show that the two triangles are congruent by the SSS postulate. You must show all work with the distance formula and each corresponding pair of sides to receive full credit. Video: How to find the distance of two points
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CAVA confirms the existence of an unavoidable conflict. The congruent coloring requires the fixed color be chosen‚ and consequently the two top rims be congruent conflict free. The focus is on these two issues. Congruence of Two Vertices Within three colors‚ two vertices (p‚ q)V(G) can be in one of the congruence relation defined as: congruent c(p) ≅ c(q)‚ the resulting color c(q) always equals the selected color for c(p). anti-congruent c(p) c(q)‚ <p‚ q>E‚ the resulting color c(q) always differs
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Think About a Plan The Polygon Angle-Sum Theorems Reasoning Your friend says she has another way to find the sum of the angle measures of a polygon. She picks a point inside the polygon‚ draws a segment to each vertex‚ and counts the number of triangles. She multiplies the total by 180‚ and then subtracts 360 from the product. Does her method work? Explain. Understanding the Problem 1. According to the Polygon Angle-Sum Theorem‚ what is the relationship between the number of sides of a polygon
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Proof Sheet Reflexive Property | A quantity is congruent (equal) to itself. a = a | Symmetric Property | If a = b‚ then b = a. | Transitive Property | If a = b and b = c‚ then a = c. | Addition Postulate | If equal quantities are added to equal quantities‚ the sums are equal. | Subtraction Postulate | If equal quantities are subtracted from equal quantities‚ the differences are equal. | Multiplication Postulate | If equal quantities are multiplied by equal quantities‚ the products
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Since the commencement of human existence‚ personal qualities such as: the pursuit of knowledge‚ the desire to expand ones horizons‚ and the inclination to establish and follow a dream‚ has significantly impacted society. From the earliest days‚ right up until the present time‚ a number of accomplishments have filled the vast expanse of time. Such accomplishments span from exemplary literary works‚ such as those of Cicero‚ Virgil‚ and Goethe; to philosophical breakthroughs of men like Rene Descartes
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A DETAILED LESSON PLAN IN MATHEMATICS FOR THIRD YEAR HIGH SCHOOL I. Learning Competencies 1. Identify the properties of parallelogram; 2. Apply the properties of parallelogram in problem solving; 3. Relate the properties of the parallelogram to the real world. II. Subject Matter: Properties of Parallelogram A. References a. Textbook: Oronce‚ O.A & Mendoza‚ M. O. E-Math(Geometry). 2007. pages 238-243 B. Instructional Media Visual Aids C. Values
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Diagonals of trapezium then‚ MN = |AB – CD| PARALLELOGRAM In a Quadrilateral‚ opposite sides are parallel to each other‚ then Quadrilateral is called Parallelogram. In Parallelogram Opposite sides are congruent In Parallelogram opposite angles are congruent. Adjacent angles are congruent to each other. In
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