Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Technical drawing wikipedia , lookup
Rotation formalisms in three dimensions wikipedia , lookup
Tessellation wikipedia , lookup
Multilateration wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Perceived visual angle wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Euler angles wikipedia , lookup
Integer triangle wikipedia , lookup
Geometry STAAR Review Video 4/State Reporting Category 2 Skill 1- Triangle Similarity Things to remember: What makes shapes similar? Angles congruent and sides proportional AA~ SAS~: (Included angle) SSS~ If you see a triangle in another triangle, draw each triangle separately and label what you know • • • • N L 2 M 1 O x+1 < 1 N x < U 9 L P 8 M T NP = _______ Similar: yes or no LN = _______ Justify: ______________ 6 S Skill 2- Right Triangles Things to remember: • The triangle has two legs that form the right angle and a hypotenuse that is across from the right angle. • Pythagorean Theorem: a2 + b2 = c2 • Special Right Triangles: 30⁰ – 60⁰ – 90⁰: x, x 3 , 2x 45⁰ - 45⁰ - 90⁰: x, x, x 2 • Can be used to find distance Skill 3- Parallelograms Things to remember: • 5 Properties of Parallelograms: 1. two sets of opposite sides are parallel 2. two sets of opposite sides are congruent 3. two sets of opposite angles are congruent 4. consecutive angles are supplementary 5. diagonals bisect each other • Parallelograms P = ℓ + w + ℓ + w or b + h + b + h B = ℓw or bh • Rectangles • P = ℓ + w + ℓ + w or b + h + b + h • B = ℓw or bh • Rhombus P = 4s B = 1 d1d2 2 • Square P = 4s B = s2 Skill 4 - Polygons Things to remember: • N – gon: general form • Polygons with names: Name Number of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Undecagon 11 Dodecagon 12 n-gon n Number of Angles 3 4 5 6 7 8 9 10 11 12 n • • • • • Regular – all sides are congruent and all angles are congruent Irregular – no side is necessarily congruent and no angle is necessarily congruent Convex – all the angles are pushing out of the shape Concave - at least one of the angles is caving in to the shape B = 1 Pa ( Special Right Triangle Rules may apply here) • • • • Apothem (a) – the distance from the center of the polygon to the midpoint of a side Radius – the distance from the center of the polygon to a vertex Sum of the interior angles: 180°(n − 2) Measure of each interior angle: 180°(n − 2) 2 n • Sum of the exterior angles for all polygons: 360⁰ • Measure of each exterior angle: 360° n Skill 5- Transformations Things to remember: • Reflection across the x-axis: (x, y) → (x, -y) • Reflection across the y-axis: (x, y) → (-x, y) • Reflection across the line y = x: (x, y) → (y, x) • Rotations: clockwise and counter-clockwise Order – how many times you rotate a picture and it looks exactly the same. Angle of Rotation - 360⁰ 𝑜𝑟𝑑𝑒𝑟 • Translation: (x + a, y + b) or (x – a, y – b) • Dilation when centered at the origin: (kx, ky) k is scale factor 𝒌(𝑟𝑖𝑠𝑒) • Dilation not centered at the origin: 𝒌(𝑟𝑢𝑛)