LG.1.G: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.
LG.1.G.1: Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations
LG.1.G.1.c: conditional statements (statement, inverse, converse, and contrapositive)
LG.1.G.3: Describe relationships derived from geometric figures or figural patterns
LG.1.G.4: Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines
LG.1.G.5: Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel
LG.1.G.6: Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180° , and the line joining the midpoints of two sides of a triangle is parallel to the third side and half it?s length
T.2.G: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.
T.2.G.1: Apply congruence (SSS ?) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification
T.2.G.2: Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)
T.2.G.3: Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems
T.2.G.4: Apply the Pythagorean Theorem and its converse in solving practical problems
T.2.G.5: Use the special right triangle relationships (30°-60°-90° and 45°-45°-90°) to solve problems
T.2.G.6: Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression
T.2.G.7: Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given including angles of elevation and angles of depression
M.3.G: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.
M.3.G.1: Calculate probabilities arising in geometric contexts
M.3.G.2: Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms
M.3.G.4: Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)
R.4.G: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
R.4.G.1: Explore and verify the properties of quadrilaterals
R.4.G.2: Solve problems using properties of polygons:
R.4.G.2.a: sum of the measures of the interior angles of a polygon
R.4.G.2.b: interior and exterior angle measure of a regular polygon or irregular polygon
R.4.G.2.c: number of sides or angles of a polygon
R.4.G.5: Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles
R.4.G.6: Solve problems using inscribed and circumscribed figures
R.4.G.7: Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects
CGT.5.G: Students will specify locations, apply transformations and describe relationships using coordinate geometry.
CGT.5.G.1: Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines
CGT.5.G.6: Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle
CGT.5.G.7: Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane
CGT.5.G.7.c: rotations (90°, 180°, clockwise and counterclockwise about the origin)
CGT.5.G.7.d: dilations (scale factor)
Correlation last revised: 3/1/2018