Pacing guides for High School Geometry courses.

- Mathematics > General
- Mathematics > Geometry

- Grade 9
- Grade 10
- Grade 11
- Grade 12

Use a variety of problem solving strategies to understand new mathematical content

Observe and explain patterns to formulate generalizations and conjectures

Use multiple representations to represent and explain problem situations (e.g., spatial, geometric, verbal, numeric, algebraic, and graphical representations)

Construct various types of reasoning, arguments, justifications and methods of proof for problems

Choose an effective approach to solve a problem from a variety of strategies (numeric, graphic, algebraic)

Use a variety of strategies to extend solution methods to other problems

Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving

Determine information required to solve a problem, choose methods for obtaining the information, and define parameters for acceptable solutions

Interpret solutions within the given constraints of a problem

Evaluate the relative efficiency of different representations and solution methods of a problem

Note: The algebraic skills and concepts within the Algebra process and content performance indicators must be maintained and applied as students are asked to investigate, make conjectures, give rationale, and justify or prove geometric concepts.

Know and apply that if a line is perpendicular to each of two intersecting lines at their point of intersection, then the line is perpendicular to the plane determined by them

Know and apply that through a given point there passes one and only one plane perpendicular to a given line

Know and apply that through a given point there passes one and only one line perpendicular to a given plane

Know and apply that two lines perpendicular to the same plane are coplanar

Know and apply that two planes are perpendicular to each other if and only if one plane contains a line perpendicular to the second plane

Know and apply that if a line is perpendicular to a plane, then any line perpendicular to the given line at its point of intersection with the given plane is in the given plane

Know and apply that if a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane

Know and apply that if a plane intersects two parallel planes, then the intersection is two parallel lines

Know and apply that if two planes are perpendicular to the same line, they are parallel

Know and apply that the lateral edges of a prism are congruent and parallel

Know and apply that two prisms have equal volumes if their bases have equal areas and their altitudes are equal

Know and apply that the volume of a prism is the product of the area of the base and the altitude

lateral edges are congruent

lateral faces are congruent isosceles triangles

volume of a pyramid equals one-third the product of the area of the base and the altitude

bases are congruent

volume equals the product of the area of the base and the altitude

lateral area of a right circular cylinder equals the product of an altitude and the circumference of the base

lateral area equals one-half the product of the slant height and the circumference of its base

volume is one-third the product of the area of its base and its altitude

the intersection of a plane and a sphere is a circle

a great circle is the largest circle that can be drawn on a sphere

two planes equidistant from the center of the sphere and intersecting the sphere do so in congruent circles

surface area is 4 pi r²

volume is 4/3 pi r³

Construct a bisector of a given angle, using a straightedge and compass, and justify the construction

Construct the perpendicular bisector of a given segment, using a straightedge and compass, and justify the construction

Construct lines parallel (or perpendicular) to a given line through a given point, using a straightedge and compass, and justify the construction

Construct an equilateral triangle, using a straightedge and compass, and justify the construction

Investigate and apply the concurrence of medians, altitudes, angle bisectors, and perpendicular bisectors of triangles

Solve problems using compound loci

Graph and solve compound loci in the coordinate plane

Determine the negation of a statement and establish its truth value

Know and apply the conditions under which a compound statement (conjunction, disjunction, conditional, biconditional) is true

Identify and write the inverse, converse, and contrapositive of a given conditional statement and note the logical equivalences

Write a proof arguing from a given hypothesis to a given conclusion

Determine the congruence of two triangles by using one of the five congruence techniques (SSS, SAS, ASA, AAS, HL), given sufficient information about the sides and/or angles of two congruent triangles

Identify corresponding parts of congruent triangles

Investigate, justify, and apply theorems about the sum of the measures of the angles of a triangle

Investigate, justify, and apply the isosceles triangle theorem and its converse

Investigate, justify, and apply theorems about geometric inequalities, using the exterior angle theorem

Investigate, justify, and apply the triangle inequality theorem

Determine either the longest side of a triangle given the three angle measures or the largest angle given the lengths of three sides of a triangle

Determine if two lines cut by a transversal are parallel, based on the measure of given pairs of angles formed by the transversal and the lines

Investigate, justify, and apply theorems about the sum of the measures of the interior and exterior angles of polygons

Investigate, justify, and apply theorems about each interior and exterior angle measure of regular polygons

Investigate, justify, and apply theorems about parallelograms involving their angles, sides, and diagonals

Investigate, justify, and apply theorems about special parallelograms (rectangles, rhombuses, squares) involving their angles, sides, and diagonals

Investigate, justify, and apply theorems about trapezoids (including isosceles trapezoids) involving their angles, sides, medians, and diagonals

Justify that some quadrilaterals are parallelograms, rhombuses, rectangles, squares, or trapezoids

Investigate, justify, and apply theorems about geometric relationships, based on the properties of the line segment joining the midpoints of two sides of the triangle

Investigate, justify, and apply theorems about the centroid of a triangle, dividing each median into segments whose lengths are in the ratio 2:1

Establish similarity of triangles, using the following theorems: AA, SAS, and SSS

Investigate, justify, and apply theorems about similar triangles

Investigate, justify, and apply theorems about proportional relationships among the segments of the sides of the triangle, given one or more lines parallel to one side of a triangle and intersecting the other two sides of the triangle

the altitude to the hypotenuse of a right triangle is the mean proportional between the two segments along the hypotenuse

the altitude to the hypotenuse of a right triangle divides the hypotenuse so that either leg of the right triangle is the mean proportional between the hypotenuse and segment of the hypotenuse adjacent to that leg

Investigate, justify, and apply the Pythagorean theorem and its converse

perpendicular bisectors of chords

the relative lengths of chords as compared to their distance from the center of the circle

a perpendicular to the tangent at the point of tangency

two tangents to a circle from the same external point

common tangents of two non-intersecting or tangent circles

inside the circle (two chords)