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
Multilateration wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Integer triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
Euler angles wikipedia , lookup
Line (geometry) wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Geometry STAAR Review Skill 1 - Transversal Lines Things to remember: Video 1/State Reporting Category 4 Transversal line – a line that intersects two or more co-planar lines. • Corresponding Angles are on the same side of a transversal and the same sides of the intersecting lines. They are congruent if the intersecting lines are parallel. • Alternate Interior Angles are on opposite sides of a transversal and inside of the intersecting lines. They are congruent if the intersecting lines are parallel. • Alternate Exterior Angles are on opposite sides of a transversal and outside of the intersecting lines. They are congruent if the intersecting lines are parallel. • Consecutive Interior Angles are on the same side of a transversal and inside of the intersecting lines. They are supplementary if the intersecting lines are parallel. Skill 2 - Triangle Properties Things to remember: **Triangle Sum THEOREM: The sum of the interior angles of any triangle is always 180°. • In the Pythagorean Theorem, a2 + b2 = c2, c is always the hypotenuse. • The rules that work to prove that two triangles are congruent are: SSS, SAS, ASA, SAA, HA, HL • Remember there is no SSA. Skill 3 - Nets of 3D Figures Things to remember: Net- A flat, 2 dimensional, picture that becomes a 3D shape when folded together. The polygons in the 2D net will become the faces of the 3D solid. • Pyramids have triangular lateral faces with 1 base. • Prisms have rectangular lateral faces with 2 bases. The two bases are congruent polygons. Skill 4 - Polyhedrons Things to remember: Polyhedron- A closed 3 dimensional figure formed by 4 or more polygons that intersect only at their edges. Think: 3D shape with polygon faces. • Euler’s Formula: The relationship between the number of vertices, edges, and faces of any polyhedron. Faces + Vertices = Edges + 2 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) Skill 6 – Quadrilaterals Things to remember: Remember the unique traits that make each quadrilateral specifically. • Parallelogram: A quadrilateral with opposite sides parallel, opposite sides ≅ , opposite angles ≅ , consecutive angles supplementary (180°), and both diagonals bisected B = bh • Rectangle: A parallelogram with at least 1 right angle, and diagonals ≅ . (4 isosceles Δ’s) B = bh • Rhombus: A parallelogram with all sides ≅ , diagonals ⊥ , and diagonals bisect each angle. (4 right Δ’s) • • • B = ½ d1d2 Square: A parallelogram, Rectangle, and Rhombus combined. No individual traits. (4 right isosceles Δ’s) B = bh Trapezoid: B = ½ (b 1 + b 2 )h Isosceles Trapezoid: Kite: B = ½ d 1 d 2 Skill 6 Continued Skill 7 - Circles Things to remember: 360⁰ in the interior and exterior of a circle 𝐶 = 𝜋𝑑 𝑜𝑟 𝐶 = 2𝜋𝑟 m arc is in degrees 2 𝐴 = 𝜋𝑟 length of arc is a measure arc • The radius is half of the diameter. • Angle on circle = ½ arc • Angle inside = ½(arc + arc) • Angle outside = ½(arc - arc) • Central angle = arc length • Two chords: (piece)(piece) = (piece)(piece) • Two secants: (whole)(outside) = (whole)(outside) • Secant and Tangent: (tangent)² = (whole)(outside) 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑎𝑟𝑐 • Length of arc: AB = = • Area of a Sector = 360° 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒 360° = 2𝜋𝑟 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟 𝜋𝑟² Skill 8 - Probability Things to remember: Chance of success All possible outcomes X 100 Skill 9 - Composite Figures Things to remember: • Composite tells you to add or subtract the shapes (Volume or Area) • Write the formulas down before you work. Composite Figures 2 dimensional - A plane figure made up of triangles, rectangles, trapezoids, circles, and other simple shapes. Composite Figures 3 dimensional - A 3-D figure made up of pyramids, prisms, cylinders, cones, spheres, or hemispheres.