PS1 Tools of Geometry: Students will be able to find distances between points and midpoints of line segments; identify angle relationships; and find perimeters, areas, surface areas and volumes. LT 1.1 Points, Lines, and Planes (*) PS2 Reasoning and Proof: Students will be able to make conjectures and find counterexamples for statements; use deductive reasoning to reach valid conclusions; and write proofs involving segment and angle theorems. LT 1.2 Linear Measure (*) LT 1.3 Distance and Midpoints (*) LT 1.4 Angle Measure (*) LT 1.5 Angle Relationships (*) LT 1.6 Two-Dimensional Figures (*) LT 1.7 Three-Dimensional Figures (*) LT 1.c Constructions LT 2.1 Industive Reasoning and Conjecture LT 2.2 Logic LT 2.3 Conditional Statements LT 2.4 Deductive Reasoning LT 2.5 Postulates and Paragraph Proofs LT 2.6 Algebraic Proof LT 2.7 Proving Segment Relationships LT 2.8 Proving Angle Relationships PS3 Parallel and Perpendicular Lines: Students will be able to identify and prove relationships that occur with parallel lines and tranversals; use slope to analyze a line and to write its equation; and find the distance between a point and a line and between two parallel lines. LT 3.1 Parallel Lines and Tranversals (*) LT 3.2 Angles and Parallel Lines (*) I can identify and model points, lines, and planes. I can identify intersecting lines and planes. I can measure segments. I can calculate with measures. I can find the distance between two points. I can find the midpoint of a segment. I can measure and classify angles. I can identify and use congruent angles and the bisector of an angle. I can identify and use special pairs of angles. I can identify perpendicular lines. I can identify and name polygons. I can find perimeter, circumference, and area of two-dimensional figures. I can identify and name three-dimensional figures. I can find surface area and volume. I can perform formal geometric constructions. I can make conjectures based on inductive reasoning. I can find counterexamples. I can determine truth values of negations, conjections, and disjunctions. I can represent conjuctions and disjunctions using Venn diagrams. I can analyze statements in if-then form and writes converses, inverses, and contrapositives. I can use the Laws of Detachment and Syllogism. I can identify and use basic postulates about points, lines, and planes and can write paragraph proofs. I can use algebra to write two-column proofs. I can use properties of equality to write geometric proofs. I can write proofs involving segment addition. I can write proofs involving congruence. I can write proofs involving supplementary and complementary angles. I can write proofs involving congruent and right angles I can identify the relationships between two lines or two planes. I can name angles pairs formed by parallel lines and transversals. I can use theorems to determine the relationships between specific pairs of angles. I can use algebra to find angle measurements.
LT 3.3 Slopes of Lines (*) LT 3.4 Equations of Lines (*) LT 3.5 Proving Lines Parallel (*) LT 3.6 Perpendiculars and Distance PS4 Congruent Triangles: Students will be able to apply special relationships about the interior and exterior angles of triangles; identify corresponding parts of congruent triangles and prove triangles congruent; and learn about the special properties of isosceles and equilateral triangles. LT 4.1 Classifying Triangles (*) LT 4.2 Angles of Triangles (*) LT 4.3 Congruent Triangles (*) LT 4.4 Proving Triangles Congruent - SSS, SAS (*) LT 4.5 Proving Triangles Congruent - ASA, AAS (*) LT 4.6 Isosceles and Equilateral Triangles (*) LT 4.7 Congruence Transformations (*) LT 4.8 Triangles and Coordinate Proof (*) PS5 Relationships in Triangles: Students will be able to learn about special segments and points related to triangles; learn about relationships between the sides and angles of triangles; and learn to write indirect proofs. LT 5.1 Bisectors of Triangles (*) LT 5.2 Medians and Altitudes of Triangles (*) LT 5.3 Inequalities in One Triangle (*) LT 5.4 Indirect Proof LT 5.5 The Triangle Inequality (*) I can find slopes of lines. I can use slope to identify parallel and perpendicular lines. I can write and equation of a lines given information about the graph. I can solve problems by writing equations. I can recognize angle pairs that occur with parallel lines. I can prove that two lines area parallel. I can find the distance between a point and a line. I can find the distance between two parallel lines. I can identify and classify triangles by angle measure and side measures. I can apply the Triangle Angle-Sum Theorem. I can apply the Exterior Angle Theorem. I can name and use corresponding parts of congruent polygons. I can prove triangles congruent using the definition of congruence. I can use the SSS and SAS Postulates to test for triangle congruence. I can use the ASA and AAS Postulates to test for triangle congruence. I can use properties of isosceles and equilateral triangles. I can identify reflections, translations, and rotations. I can verify congruence after a congruence transformations I can position and label triangles for use in coordinate proofs. I can write coordinate proofs. I can identify and use perpendicular bisectors in triangles. I can identify and use angle bisectors in triangles. I can identify and use medians in triangles. I can identify and use altitudes in triangles. I can recognize and apply properties of inequalities to the measures of the angles of a triangle. I can recognize and apply properties of inequalities to the relationships between the angles and the sides of a triangle. I can write indirect algebra proofs. I can write indirect geometric proofs. I can use the Triangle Inequality Theorem to identify possible triangles. I can prove triangle relationships using the Triangle Inequality Theorem.
LT 5.6 Inequalities in Two Triangles PS6 Quadrilaterals: Students will be able to find and use the sum of the measures of interior and exterior angles of a polygon; recognize and apply properties of quadrilaterals; and compare quadrilaterals. LT 6.1 Angles of Polygons PS7 Proportions and Similarity: Students will be able to identify similar polygons and use ratios and proportions to solve problems; identify and apply similarity transformations; and use scale models and drawings to solve problems. LT 6.2 Parallelograms (*) LT 6.3 Tests for Parallelograms (*) LT 6.4 Rectangles (*) LT 6.5 Rhombi and Squares (*) LT 6.6 Trapezoids and Kites (*) LT 7.1 Ratios and Proportions LT 7.2 Similar Polygons (*) LT 7.3 Similar Triangles (*) LT 7.4 Parallel Lines and Proportional Parts (*) LT 7.5 Parts of Similar Triangles (*) LT 7.6 Similarity Transformations (*) LT 7.7 Scale Drawings and Models (*) PS8 Right Triangles and Trigonometry: Students will be able to use the Pythagorean Theorem; use properties of special right triangles; and use trigonometry to find missing measures of triangles. LT 8.1 Geometric Mean (*) I can apply the Hinge Theorem or its converse to make comparisons in two triangles. I can prove triangle relationships using the Hinge Theorem or its convers. I can find and use the sum of the measures of the interior angles of a polygon. I can find and use the sum of the measures of the exterior angles of a polygon. I can recognize and apply the properties of the sides and angles of parallelograms. I can recognize and apply the properties of teh diagonals of parallelograms. I can recognize the conditions that ensure a quadrilateral is a parallelogram. I can prove that a set of points form a parallelogram in the coordinate plane. I can recognize and apply properties of rectangles. I can determine whether parallelograms are rectangles. I can recognize and apply properties of rhombi and squares. I can determine whether quadrilaterals are rectangles, rhombi, or squares. I can recognize and apply the properties of trapezoids, including the medians of trapezoids. I can recognize and apply the properties of kites. I can write ratios. I can write and solve proportions. I can use proportions to identify similar polygons. I can solve problems using the properties of similar polygons. I can identify similar triangles using the AA Similarity Postulate and the SSS and SAS Simliarity Theorems. I can use similar triangles to solve problems. I can use proportional parts within triangles. I can use proportional parts with parallel lines. I can recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles. I can use the Triangle Bisector Theorem. I can identify similarity transformations. I can verify similarity after a simliarity transformation. I can interpret scale models. I can use scale factors to solve problems. I can find the geometric mean between two numbers. I can solve problems involving relationships between parts of a right triangles and the altitude to its hypotenuse.
LT 8.2 The Pythagorean Theorem and Its Converse (*) LT 8.3 Special Right Triangles (*) LT 8.4 Trigonometry (*) LT 8.5 Angles of Elevation and Depression LT 8.6 The Law of Sines and Cosines LT 8.7 Vectors PS9 Transformations and Symmetry: Students will be able to name and draw figures that have been reflected, translated, rotated, or dilated; recognize and draw compositions of transformations; and identify symmetry in two- and threedimensional figures. LT 9.1 Reflections (*) PS10 Circles: Students will be able to learn the relationships between central angles, arcs, and inscribed angles in a circle; define and use secants and tangents; and use an equation to identify or describe a circle. LT 9.2 Translations (*) LT 9.3 Rotations (*) LT 9.4 Compositions of Transformations LT 9.5 Symmetry (*) LT 9.6 Dilations (*) LT 10.1 Circles and Circumference LT 10.2 Measuring Angles and Arcs LT 10.3 Arcs and Chords LT 10.4 Inscribed Angles I can use the Pythagorean Theorem. I can use the Converse of the Pythagorean Theorem. I can use the properties of 45-45-90 triangles. I can use the properties of 30-60-90 triangles. I can find trigonometric ratios using right triangles. I can use trigonometric ratios to find angle measures in right triangles. I can solve problems involving angles of elevation and depression. I can use angles of elevation and depression to find the distance between two objects. I can use the Law of Sines to solve triangles. I can use the Law of Cosines to solve triangles. I can perform vector operations geometrically. I can perform vector operations on the coordinate plane. I can draw reflections. I can draw reflections in the coordinate plane. I can draw translations. I can draw translations in the coordinate plane. I can draw rotations. I can draw rotations in the coordinate plane. I can draw glide reflections and other compositions of isometries in the coordinate plane. I can draw compositions of reflections in parallel and intersecting lines. I can identify line and rotational symmetries in two-dimensional figures. I can identify plane and axis symmetries in three-dimensional figures. I can draw dilations. I can draw dilations in the coordinate plane. I can identify and use parts of circles. I can solve problems involving the circumference of a circle. I can identify central angles, major arcs, minor arcs, and semicircles, and find their measures. I can find arc lengths. I can recognize and use relationships between arcs and chords. I can recognize and use relationships between arcs, chords, and diameters. I can find measures of inscribed angles. I can find measures of inscribed polygons.
LT 10.5 Tangents LT 10.6 Secants, Tangents, and Angle Measures LT 10.7 Special Segments in a Circle LT 10.8 Equations of Circles PS11 Areas of Polygons and Circles: Students will be able to find areas of polygons; solve problems involving areas and sectors of circles; and find scale factors using similar figures. LT 11.1 Areas of Parallelograms and Triangles (*) PS12 Extending Surface Area and Volume: Students will be able to find lateral areas, surface areas, and volumes of various solid figures; investigate Euclidean and spherical geometries; and use properties of similar solids. LT 11.2 Areas of Trapezoids, Rhombi, and Kites (*) LT 11.3 Areas of Circles and Sectors (*) LT 11.4 Areas of Regular Polygons and Composite Figures (*) LT 11.5 Areas of SImilar Figures (*) LT 12.1 Representations of Three-Dimensional Figures LT 12.2 Surface Areas of Prisms and Cylinders (*) LT 12.3 Surface Areas of Pyramids and Cones (*) LT 12.4 Volumes of Prisms and Cylinders (*) LT 12.5 Volumes of Pyramids and Cones (*) LT 12.6 Surface Areas and Volumes of Spheres (*) LT 12.7 Spherical Geometry LT 12.8 Congruent and Similar Solids I can use properties of tangents. I can solve problems involving circumscribed polygons. I can find measures of angles formed by lines intersecting on or inside a circle. I can find measures of angles formed by lines intersecting outside the circle. I can find measures of segments that intersect in the interior of a circle. I can find measures of segments that intersecct in the exterior of a circle. I can write an equation of a circle. I can graph a circle on the coordinate plane. I can find perimeters and areas of parallelograms. I can find perimeters and areas of triangles. I can find areas of trapezoids. I can find areas of rhombi and kites. I can find areas of circles. I can find areas of sectors of circles. I can find areas of regular polygons. I can find areas of composite figures. I can find areas of similar figures using scale factors. I can find scale factors or missing measures given the areas of similar figures. I can draw isometric views of three-dimensional figures. I can investigate cross sections of three-dimensional figures. I can find lateral areas and surface areas of prisms. I can find lateral areas and surface areas of cylinders. I can find lateral areas and surface areas of pyramids. I can find lateral areas and surface areas of cones. I can find volumes of prisms. I can find volumes of cylinders. I can find volumes of pyramids. I can find volumes of cones. I can find surface areas of spheres. I can find volumes of spheres. I can describe sets of points on a sphere. I can identify congruent or similar solids. I can use properties of similar solids.
PS13 Probability and Measurement: Students will be able to represent sample spaces; use permutations and combinations I can use lists, tables, and tree diagrams to represent sample with probability; find probabilities by using length and area; spaces. and find probability of compound events. LT 13.1 Representing Sample Spaces I can use the Fundamental Counting Principle to count outcomes. LT 13.2 Probability with Permutations and Combinations LT 13.3 Geometric Probability LT 13.4 Simulations LT 13.5 Probabilities of Independent and Dependent Events LT 13.6 Probabilities of Mutually Exclusive Events (*) - indicates Key Learning Target I can use permutations with probability. I can use combinations with probability. I can find probabilities by using length. I can find probabilities by using area. I can design simulations to estimate probabilities. I can summarize data from simulations. I can find probabilties of independent and dependent events. I can find probabilties of events given the occurrence of other events. I can find probabilties of events that are mutually exclusive and events that are not mutually exclusive. I can find probabilties of complements.