### Curriculum Completed Through March 13,2020

 Geometric Thinking and Vocabulary Focus Topics Standards of Learning The student will use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include Identify the converse, inverse, and contrapositive of a conditional statement. (a) Translate verbal arguments into symbolic form using the symbols of formal logic. (b) Determine that the validity of a logical argument using valid forms of deductive reasoning. (c) Determine that an argument is false using a counterexample. (c) G.1 abc

 Angle Relationships with Intersecting and Parallel Lines The student will use the relationships between angles formed by two lines intersected by a transversal to Prove two or more lines are parallel given angle measurements expressed numerically or algebraically. (a) Prove two lines are parallel using deductive proofs given relationships between and among angles. (a) Solve problems by using the relationships between pairs of angles formed by the intersection of two parallel lines and a transversal including corresponding angles, alternate interior angles, alternate exterior angles, same-side (consecutive) interior angles, and same-side (consecutive) exterior angles. (b) Solve problems, including practical problems, involving intersecting and parallel lines. (b) The student will Construct and justify the constructions of a perpendicular to a given line from a point not on the line; a perpendicular to a given line at a given point on the line; and a line parallel to a given line through a point not on the given line; (g) G.2 ab                 G.4 cdg

 Triangle Relationships The student, given information concerning the lengths of sides and/or measures of angles in triangles, will solve problems, including practical problems. This will include Given information about the lengths of sides and/or measures of angles in triangles, solve problems, including practical problems. (a, b, c, d) Order the sides of a triangle by their lengths when given information about the measures of the angles. (a) Order the angles of a triangle by their measures when given information about the lengths of the sides. (b) Given the lengths of three segments, determine whether a triangle could be formed. (c) Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie. (d) G.5 abcd

 Congruent Triangles The student, given information in the form of a figure or statement, will prove two triangles are congruent. Prove two triangles congruent given relationships among angles and sides of triangles expressed numerically or algebraically. Prove two triangles congruent given representations in the coordinate plane and using coordinate methods (distance formula and slope formula). Use direct proofs to prove two triangles congruent. G.6

 Similar Triangles The student, given information in the form of a figure or statement, will prove two triangles are similar. Prove two triangles similar given relationships among angles and sides of triangles expressed numerically or algebraically. Prove two triangles similar given representations in the coordinate plane and using coordinate methods (distance formula and slope formula). Use direct proofs to prove triangles similar. G.7

 Right Triangles and Special Right Triangles The student will solve problems, including practical problems, involving right triangles. This will include applying. Solve problems, including practical problems, using right triangle trigonometry and properties of special right triangles. (a, b, c) Solve for missing lengths in geometric figures, using properties of 45°-45°-90° triangles where rationalizing denominators may be necessary. (b) Solve for missing lengths in geometric figures, using properties of 30°-60°-90° triangles where rationalizing denominators may be necessary. (b). Solve problems, including practical problems, involving right triangles with missing side lengths or angle measurements, using sine, cosine, and tangent ratios. (c) The student will solve problems, including practical problems, involving right triangles. This will include applying the Pythagorean Theorem and its converse; Solve problems, including practical problems, using right triangle trigonometry and properties of special right triangles. (a, b, c) Determine whether a triangle formed with three given lengths is a right triangle. (a) G.8 bc                 G.8a

 Quadrilaterals and Polygons The student will verify and use properties of quadrilaterals to solve problems, including practical problems. Solve problems, including practical problems, using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, and trapezoids. Prove that quadrilaterals have specific properties, using coordinate and algebraic methods, such as the distance formula, slope, and midpoint formula. Prove the properties of quadrilaterals, using direct proofs.   The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the Solve problems, including practical problems, involving angles of convex polygons. (a, b, c) Determine the sum of the measures of the interior and exterior angles of a convex polygon. (a) Determine the measure of each interior and exterior angle of a regular polygon. (b) Determine the number of sides of a regular polygon, given the measures of interior or exterior angles of the polygon. G.9              G.10abc