B2C2 = sqrt(((2 (2))^2) + ((7 1)^2)) = 6 BC = sqrt(((6 6)^2) + ((3 (3))^2)) = 6 B2C2 = BC Triangle A2B2C2 = Triangle ABC by construction. Reflection A’ (4‚ 1) B’ (4‚ 6) C’ (4‚ 6) Line of reflection is x=y Angle A2 = Angle C by construction. Angle C2 = Angle A by construction. AC = sqrt(((4 (4))^2) + ((5 (1))^2)) = 10 A2C2 = sqrt(((6 (2))^2) + ((3 ( 3))^2)) = 10 AC = A2C2 Triangle A2C2B2 = Triangle ACB by construction. Rotation A’ (2‚ 3) B’ (6‚ 3) C’ (6‚ 3) A2C2 = sqrt(((6 2)^2) + ((3 3)^2)) = 10
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parallel lines are cut by a transversal • the corresponding angles are equal (4 pairs) • the alternate angles are equal (2 pairs) • the co-interior angles are supplementary (sum to 180°) (2 pairs). A triangle with vertices A‚ B and C is written Δ ABC. ■■ The minimal conditions for a unique triangle are: • SSS (3 sides) • SAS (2 sides and the included angle) • ASA (2 angles and the side between)Key ideas • AAS (2 angles and a side not between) • RHS (a right angle‚ the hypotenuse and another side)
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and a vertex. 16. The distance around the circle. 17. A space figure with two circular bases that are congruent and parallel. 18. A chord that contains the center of the circle. 19. A quadrilateral with two distinct pairs of congruent and adjacent sides. 20. A pair of adjacent angles whose uncommon sides are opposite rays. 21. A segment from the vertex of the triangle to the midpoint of the opposite side. 22. Are coplanar lines that do not intersect. 23. A quadrilateral
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book Veritical angle congruence → triangle exterior angle → AAS → transversal making parallel lines → alternate angles → three angles being equal to two right angles → PYTHAGOREAN THEOREM Proposition I.47 In right angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle. Euclid’s diagram became known as the “Windmill” because of the resemblance. Carl Friedrich Gauss thought that triangles had to be less or more than 180
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Math Review for the Quantitative Reasoning Measure of the GRE® revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important to understand in order to solve problems and to reason quantitatively on the Quantitative Reasoning measure of the GRE revised General Test. The following material includes many definitions‚ properties‚ and examples‚ as well as a set of exercises (with answers) at the end of each review
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Math Review for the Quantitative Reasoning Measure of the GRE® revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important to understand in order to solve problems and to reason quantitatively on the Quantitative Reasoning measure of the GRE revised General Test. The following material includes many definitions‚ properties‚ and examples‚ as well as a set of exercises (with answers) at the end of each
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(Mental Ability) : Rational Numbers‚ Exponents and Powers‚ Direct and Inverse Variations‚ Comparing Quantities‚ Algebraic Expressions and Identities‚ Factorization of Algebraic Expressions‚ Linear Equations in One Variable‚ More About Triangles‚ Congruent Triangles‚ Understanding Quadrilaterals‚ Mensuration‚ Data Handling‚ Visualising Solid Shapes‚ Introduction to Graphs‚ Playing with Numbers‚ Squares and Square Roots‚ Cubes and Cube Roots‚ Problem Based on Figures‚ Odd One Out‚ Series Completion
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JAMES RUSE AGRICULTURAL HIGH SCHOOL MATHEMATICS PROGRAMME YEAR 10 – 2011 LIST OF TOPICS TOPIC 1 – ALGEBRA REVISION TOPIC 2 – GEOMETRY PROOFS REVISION: PART 1 TOPIC 3 – CO-ORDINATE GEOMETRY TOPIC 4 – VARIATION TOPIC 5 – GEOMETRY PROOFS REVISION: PART 2 TOPIC 6 – TRIGONOMETRY TOPIC 7 – GEOMETRY PROOFS TOPIC 8 – PROBABILITY REVISION TOPIC 9 – GRAPHING REVISION TOPIC 10 – FURTHER GRAPHS TOPIC 11 – TRIGONOMETRIC EQUATIONS AND IDENTITIES TOPIC 12 – GENERAL REFERENCE and YEARLY REVISION
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rectangle is my name My 4 sides are not the same 2 are short and 2 are long Count my sides‚ come along 1-2-3-4 Ollie Oval I am Ollie Oval A football shape is mine Some people think that I’m an egg But I think I look fine! Tommy Triangle Tommy triangle is the name for me. Tap my sides 1‚ 2‚ 3. Harry Heart Harry Heart is my name The shape I make is my fame With a point on the bottom And two humps on top When it comes to love I just
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Honors Geometry – EOC Review Study Guide | | | |Chapter 1 – Tools of Geometry |Chapter 2 – Logic and Reasoning | | | | |[pic]
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