Geometry Learning Targets

Transcription

1 Geometry Learning Targets

2 G0. Algebra Prior Knowledge G0a. Simplify algebraic expressions. G0b. Solve a multi-step equation. G0c. Graph a linear equation or find the equation of a line. G0d. Use the distributive property to multiply binomials. G0e. Solve a quadratic function using the quadratic formula and/or factoring. G0f. Solve a linear system of equations. G0g. Use slope to determine if lines are parallel or perpendicular. G0h. Write and solve a proportional equation. G0i. Write and graph exponential functions. G0j(+) Simplify radicals and rationalize the denominator. G1. Transformations I can apply I can extend G1a. I can draw rigid transformations. ü Reflections ü Rotations ü Translations ü Combinations of reflections, rotations, and translations ü Reflection and Rotation Symmetry ü Predict the composition of transformation that will map a figure onto a congruent figure. ü coordinate rules to transformations

3 G2. Lines & Angles I can apply I can extend G2a. I can use theorems, postulates, or definitions about lines and angles. ü Transversals, alternate interior, corresponding, sameside interior ü Linear angles/straight angles, vertical, complementary, and supplementary ü Triangle sum theorem ü Given an angle relationship, prove that two lines are parallel G3. Similarity I can apply I can extend G3a. I can determine that two figures are similar. ü AA~ ü SSS~ ü SAS~ ü Scale Factors ü Dilations ü Perform dilation with a given center and scale factor. ü To find missing parts of similar figures including right triangles ü Real world similar triangle problems ü Explain why SSA~ does not prove two triangle are similar

4 G4. Trigonometry I can apply I can extend G4a. I can use appropriate tools to find missing sides and angles in right triangles. ü Sine ü Cosine ü Tangent ü Pythagorean Theorem ü Inverse Trigonometric Functions ü Real world right triangle problems ü The use of slope triangles to identify slope triangles, sides and angles ü The relationship between the sin and cos of complementary angles ü (+) Law of Sin, Law of Cos

5 G5. Triangles & Quadrilaterals: Application & Proof G5a. I can justify that two triangles are congruent. I can apply ü SSS/SAS/ASA/AAS/HL ü CPCTC ü 2 column proof, flow charts I can extend ü I can identify and explain that in a pair of congruent triangles, corresponding sides are congruent and corresponding angles are congruent. ü I can use theorems, postulates, or definitions to prove theorems about parallelograms ü Opposite sides and angles of a parallelogram are congruent, ü Diagonals of a parallelogram bisect each other; rectangles have congruent diagonals ü (+) Base angles of isosceles triangles; triangle midsegment; and medians in triangles.

6 G6. Coordinate Geometry I can apply I can extend G6a. I can use coordinates of the vertices to compute perimeter and area. G6b. I can justify a claim about a figure using the coordinate grid. ü Distance formula ü Pythagorean theorem ü Area formulas ü Distance formula, midpoint formula, Pythagorean theorem ü Parallel lines, perpendicular lines, negative reciprocals ü Properties of quadrilaterals ü (+)I can calculate the point(s) on a directed line segment that partitions the line segment into a given ratio.

7 G7. Circles I can apply I can extend G7a. I can apply the properties of angles within circles. G7b. I can calculate the area of a sector and arc length. G7c I can identify the center and radius of a circle given its equation. ü Central angles, inscribed and circumscribed angles ü Tangents, arcs and intersecting chords ü Using the ratio of the intercepted arc (central angle) measure and 360. ü Convert equation from general to standard ü Completing the square ü Properties of geometric figures to comparable realworld objects. ü (+) I can prove that opposite angles in an inscribed quadrilateral are supplementary ü (+) I can use pictures to explain that a regular polygon with many sides is nearly a circle and its perimeter is nearly the circumference of a circle.

8 G8. Geometric Modeling and Constructions G8a. I can apply geometric concepts in modeling situations. G8b. I can use tools and methods to create constructions. I can apply ü Precisely copy an angle, ü Bisect a segment, ü Bisect an angle, ü Construct perpendicular lines and bisectors ü Construct a line parallel to a given line through a point not on the line. I can extend ü Solve design problems using a geometric model. ü Apply concepts of density based on area and volume, including converting units of measure ü Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. ü (+) Construct the inscribed and circumscribed circles of a triangle.

9 G9. Solids & Conics I can apply I can extend G9a. I can calculate the volume of a prism, cylinder, cone, pyramid and sphere. G9b. I can identify the shapes of twodimensional cross-sections of threedimensional objects. ü Using the given formula v = B h and the volume of a cylinder V = πr 2 h. ü Identify shapes as ellipse, arc, circle, oval ü Explain that the volume of a pyramid is 1/3 the volume of a prism with the same base area and height. ü Use volume formula for cylinders, pyramids, cones and spheres to solve real life problems ü (+) Identify the focus and directrix of a parabola when given its equation.

10 G10. Conditional Probability G10a. I can calculate probabilities with unions and intersections. G10b. I can calculate conditional & independent probabilities. I can apply ü Establish events as subsets of a sample space based on the union, intersection ü Complement of other events ü And or not ü Area models, tree diagrams ü How to identify the difference between conditional and independent events ü Area model for conditional probability ü Two-way table I can extend ü Explain that conditional probability is the probability of an event occurring given the occurrence of some other event and give examples that illustrate conditional probabilities