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Pacing guides for High School Geometry courses.

Subjects:

• Mathematics > General
• Mathematics > Geometry

Keywords:

geometry curriuculum curricula

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MA.9-12.G.PS.1: Mathematics

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

MA.9-12.G.PS.2: Mathematics

Observe and explain patterns to formulate generalizations and conjectures

MA.9-12.G.PS.3: Mathematics

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

MA.9-12.G.PS.4: Mathematics

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

MA.9-12.G.PS.5: Mathematics

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

MA.9-12.G.PS.6: Mathematics

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

MA.9-12.G.PS.7: Mathematics

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

MA.9-12.G.PS.8: Mathematics

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

MA.9-12.G.PS.9: Mathematics

Interpret solutions within the given constraints of a problem

MA.9-12.G.PS.10: Mathematics

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

MA.9-12.: Mathematics

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.

MA.9-12.G.G.1: Mathematics

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

MA.9-12.G.G.2: Mathematics

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

MA.9-12.G.G.3: Mathematics

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

MA.9-12.G.G.4: Mathematics

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

MA.9-12.G.G.5: Mathematics

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

MA.9-12.G.G.6: Mathematics

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

MA.9-12.G.G.7: Mathematics

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

MA.9-12.G.G.8: Mathematics

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

MA.9-12.G.G.9: Mathematics

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

MA.9-12.G.G.10: Mathematics

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

MA.9-12.G.G.11: Mathematics

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

MA.9-12.G.G.12: Mathematics

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

MA.9-12.G.G.13.a: Mathematics

lateral edges are congruent

MA.9-12.G.G.13.b: Mathematics

lateral faces are congruent isosceles triangles

MA.9-12.G.G.13.c: Mathematics

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

MA.9-12.G.G.14.a: Mathematics

bases are congruent

MA.9-12.G.G.14.b: Mathematics

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

MA.9-12.G.G.14.c: Mathematics

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

MA.9-12.G.G.15.a: Mathematics

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

MA.9-12.G.G.15.b: Mathematics

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

MA.9-12.G.G.16.a: Mathematics

the intersection of a plane and a sphere is a circle

MA.9-12.G.G.16.b: Mathematics

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

MA.9-12.G.G.16.c: Mathematics

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

MA.9-12.G.G.16.d: Mathematics

surface area is 4 pi r²

MA.9-12.G.G.16.e: Mathematics

volume is 4/3 pi r³

MA.9-12.G.G.17: Mathematics

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

MA.9-12.G.G.18: Mathematics

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

MA.9-12.G.G.19: Mathematics

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

MA.9-12.G.G.20: Mathematics

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

MA.9-12.G.G.21: Mathematics

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

MA.9-12.G.G.22: Mathematics

Solve problems using compound loci

MA.9-12.G.G.23: Mathematics

Graph and solve compound loci in the coordinate plane

MA.9-12.G.G.24: Mathematics

Determine the negation of a statement and establish its truth value

MA.9-12.G.G.25: Mathematics

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

MA.9-12.G.G.26: Mathematics

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

MA.9-12.G.G.27: Mathematics

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

MA.9-12.G.G.28: Mathematics

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

MA.9-12.G.G.29: Mathematics

Identify corresponding parts of congruent triangles

MA.9-12.G.G.30: Mathematics

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

MA.9-12.G.G.31: Mathematics

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

MA.9-12.G.G.32: Mathematics

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

MA.9-12.G.G.33: Mathematics

Investigate, justify, and apply the triangle inequality theorem

MA.9-12.G.G.34: Mathematics

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

MA.9-12.G.G.35: Mathematics

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

MA.9-12.G.G.36: Mathematics

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

MA.9-12.G.G.37: Mathematics

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

MA.9-12.G.G.38: Mathematics

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

MA.9-12.G.G.39: Mathematics

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

MA.9-12.G.G.40: Mathematics

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

MA.9-12.G.G.41: Mathematics

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

MA.9-12.G.G.42: Mathematics

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

MA.9-12.G.G.43: Mathematics

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

MA.9-12.G.G.44: Mathematics

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

MA.9-12.G.G.45: Mathematics

Investigate, justify, and apply theorems about similar triangles

MA.9-12.G.G.46: Mathematics

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

MA.9-12.G.G.47.a: Mathematics

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

MA.9-12.G.G.47.b: Mathematics

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

MA.9-12.G.G.48: Mathematics

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

MA.9-12.G.G.49.a: Mathematics

perpendicular bisectors of chords

MA.9-12.G.G.49.b: Mathematics

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

MA.9-12.G.G.50.a: Mathematics

a perpendicular to the tangent at the point of tangency

MA.9-12.G.G.50.b: Mathematics

two tangents to a circle from the same external point

MA.9-12.G.G.50.c: Mathematics

common tangents of two non-intersecting or tangent circles

MA.9-12.G.G.51.a: Mathematics

inside the circle (two chords)
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