Geometry at a Glance
Unit 1: The Pythagorean Theorem and Right Triangle Trigonometry Simplifying radicals Simplifying radical expressions that contain addition, subtraction, multiplication, and division Pythagorean Theorem, Pythagorean Triples, using the converse of the Pythagorean Theorem Solving applied problems involving the Pythagorean Theorem Derive the Distance Formula using the Pythagorean Theorem Applications involving the use of the Distance Formula Applications involving the use of the Midpoint Formula Derive the equation of circle Use completing the square to find the radius and center of a circle on a coordinate plane Solve problems involving circles on the coordinate plane Use properties of 45°-45°-90° triangles to solve problems Use properties of 30°-60°-90° triangles to solve problems Define trigonometric ratios and solve problems involving right triangles Explain and use the relationship between the sine and cosine of complementary angles Solve applied problems that involve angle of elevation and angle of depression Derive the formula A = 1/2 ab sin C for the area of a triangle Apply the Law of Sines and the Law of Cosines to find unknown measurements in non-right triangles
Unit 2: 2-D Figures Vocabulary introduction: triangles, parallelograms, rectangles, rhombi, squares, trapezoids, kites, circles Prove the Pythagorean Theorem using Bhaskara's and Garfield's methods Computing area and perimeter of these figures on an off the coordinate plane (including Heron's Formula) Area of sectors and arc length Area of 2D composite figures Geometric probability, and area of shaded regions including problems that involve algebraic expressions Use vocabulary to classify polygons by angles and by sides Determine the sum of the interior and exterior angles of a polygon, and the number of diagonals Define central angle, apothem, and radius as related to regular polygons Calculate the area of regular polygons
Unit 3: 3D Figures Recognize polyhedra and their parts; visuallize cross sections of space figures; create nets of solids Calculate surface area and lateral area Caculate surface area of composite solids Volume of prisms, cylinders, pyramids, cones, spheres, and composite solids Describe what happens to the perimeter, area, SA, and/or volume change if one given condition was increased, decreased, doubled, etc
Unit 4: Foundations of Geometry Know precise definitions (or descriptions) of geometric terms including point, line, line segment, ray, plane, collinear, adjacent, between, vertical angles, linear pair, parallel, perpendicular, complementary, supplementary, midpoint Review of equations of parallel and perpendicular lines on a coordinate plane **To be done through an algebra review, not during class time.** Identify special angle pairs created with two lines and a transversal Special angle pair relationships when lines are parallel (ie. If a transversal intersects two parallele lines, then alternate interior angles are congruent) and proving lines parallel Geometric constructions including copying a segment/angle, bisecting a segment/angle, constructing a perpendicular bisector of a line segment Geometric constructions and proof of parallel/perpendicular lines
Unit 5: Transformations Define the rigid transformations: translations, reflections, rotations; use notation Use and apply vector and coordinate notation to describe translations Apply the coordinate rules for reflections about the x-axis, y-axis, and the lines y = x and y = -x Use symmetry to describe reflections that map a figure onto itself Apply the coordinate rules for rotations about origin in 90° increments in clockwise and CCW directions Use symmetry to describe rotations that map a figure onto itself Constructions - finding a line of reflection given the preimage and image, construct rotations State a sequence of transformations that will move a given figure onto another Properties of dilations
Unit 6: Circles Identify and describe relationships among central and inscribed angles, radii, chords, tangent lines, and secants Construct a tangent line from a point outside a given circle to the circle Prove that all circles are similar Properties of quadrilaterals inscribed in a circle Construct inscribed and circumscribed circles of triangles Construct regular polygons (square and hexagon) which are inscribed in a circle
Unit 7: Reasoning Structure of a conditional statement Various forms of a conditional: converse, inverse, contrapositive and logical equivalence Make conjectures and provide counterexamples Write proofs involving segments and angles; should include proving Vertical Angles Theorem, proofs involving parallel lines and special angle pairs
Unit 8: Congruent Triangles Compare corresponding parts of a triangles to determine congruency; use rigid transformations to describe how one figure maps onto the other Methods for proving triangles congruent: SSS, SAS, ASA, AAS, HL Identify the missing congruence needed to prove the triangles congruent using the given method Congruent parts of congruent triangles are congruent (CPCTC) Prove line and angle theorems: Perpendicular Bisector Theorem and Angle Bisector Theorem Prove triangle theorems: Base Angles Theorem, Midsegment Theorem
Unit 9: Similar Triangles Determine if two triangles are similar by using the definition of similarity Establish AA, SSS, and SAS triangle similarity using dilations Solve applied problems that involve similarity Prove theorems related to similarity (i.e. proportions in triangles) Ratios of perimeters, areas, and volume of similar figures/solids
Unit 10: Quadrilaterals Properties of parallelograms, rectangles, rhombi, and squares on and off the coordinate plane