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
  1. a perpendicular to a given line from a point not on the line;
  2. a perpendicular to a given line at a given point on the line; and
  1. 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

    1. 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