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Course: Mathematics 300 Plane Geometry
and Introduction to Algebra
Grade 9
MATH 300 Geometry
1 credit
5 days per week; 1 year
Taught in English
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This is a required class for all 9 grade students in the Mexican and/or U.S. diploma program. Course content includes the
study of: points lines and planes, parallel lines and planes, congruent triangles, similar polygons, right triangles, circles, and
coordinate geometry. Proofs will be introduced but not emphasized.
Textbook:
Practice Book:
Bass, Laurie E., et. al. Geometry. Prentice Hall: Upper Saddle River, NJ
(2004 Edition)
All-in-One Student Workbook
Textbook:
Bellman, Allan E. Algebra 2. Prentice Hall: Upper Saddle River, NJ (2004 Edition).
Prerequisite:
MATH 200
Benchmark Code-Subject: Geometry = GEO; Algebra = A
Strand 1: Geometric Representations
Strand 2: Reasoning in Geometric Situations
Strand 3: Using Perpendicular and Perpendicular Lines
Strand 4: Similarity, Congruence and Right Triangles Trigonometry
Strand 5: Quadrilaterals
Strand 6: Area
Strand 7: Three-Dimensional Geometry
Strand 8: Circles
Strand 9: Tools of Algebra
Strand 10: Functions, Equations and Graphs
Strand 11: Linear Systems
Code: Subject.Grade.Strand#.Benchmark#
Example: GEO.9.1.4.3 – Geometry, Grade 9th, Strand 1, Standard 4, Benchmark 3
Strand 1: Geometric Representations
Standard 1: The student reviews the coordinate plane to help him/her make logical transition from
algebra to geometry and to identify, describe, and compare points, lines and planes to be used to
define other geometric terms such as angles, segments and rays.
Benchmark Code
Benchmark
GEO.9.1.1.1
GEO.9.1.1.2
GEO.9.1.1.3
GEO.9.1.1.4
GEO.9.1.1.5
Revised June 2011
The student will graph ordered pairs on a coordinate plane.
The student will identify collinear points.
The student will identify and model points, lines and planes.
The student will identify coplanar points and intersecting lines and planes.
The student will solve problems by listing the possibilities and by using
formulas.
GEO.9.1.1.6
GEO.9.1.1.7
GEO.9.1.1.8
GEO.9.1.1.9
GEO.9.1.1.10
GEO.9.1.1.11
GEO.9.1.1.12
GEO.9.1.1.13
The student will calculate maximum area of a rectangle for a given
perimeter.
The student will calculate distance between two points on a number line and
between two points in a coordinate plane.
The student will use the Pythagorean Theorem to find the length of the
hypotenuse.
The student will identify and classify angles.
The student will use the angle addition postulate to find the measures of
angles.
The student will identify and use congruent angles and the bisector of an
angle.
The student will identify and use adjacent, vertical, complementary,
supplementary and linear pairs of angles and perpendicular lines.
The student will make inferences to determine what information can and
cannot be assumed from a diagram.
GEO.9.1.1.14
GEO.9.1.1.15
The student will learn basic constructions.
The student will find and calculate perimeter, circumference and area of
polygons and circles.
Strand 2: Reasoning in Geometric Situations
Standard 1: The student explores inductive and deductive reasoning strategies leading to a study of
if-then statements and their logic and conditional statements, their inverses, their converses, and
contra-positives.
Benchmark Code
Benchmark
GEO.9.2.1.1
GEO.9.2.1.2
The student will make conjectures based on inductive reasoning.
The student will write a statement in "if-then" form with the converse,
inverse, and contra-positive of the same if-then statement.
GEO.9.2.1.3
The student will identify and use basic postulates about points, lines, and
planes.
GEO.9.2.1.4
The student will prove that angles are congruent.
Strand 3: Using Perpendicular and Parallel Lines
Standard 1: The student states the relationship between points, lines, angles, planes, spheres, parallel
lines, and slopes as well as the angle measures formed when lines intersect.
Benchmark Code
Benchmark
GEO.9.3.1.1
The student will solve problems by drawing a diagram and identifying the
relationships between two lines or two planes and naming angles formed by a
pair of lines and a transversal.
GEO.9.3.1.2
The student will find the measures of the angles formed by two parallel lines
and a transversal.
GEO.9.3.1.3
GEO.9.3.1.4
Revised June 2011
The student will use the properties of parallel lines to determine angle
measures.
The student will find the slopes of lines and use it to identify parallel and
perpendicular lines.
GEO.9.3.1.5
The student will recognize angle conditions that produce parallel lines and
prove two lines are parallel based on given angle relationships.
GEO.9.3.1.6
The student will recognize and use distance relationships among points,
lines, and planes.
GEO.9.3.1.7
The student will find a distance between a point and a line.
GEO.9.3.1.8
The student will use the polygon angle-sum theorem to find internal and
external angles.
GEO.9.3.1.9
The student will construct parallel and perpendicular lines.
Strand 4: Similarity, Congruence and Right Triangle Trigonometry
Standard 1: The student uses Algebra skills to solve proportions and identify similar figures and
solve problems using proportions.
Benchmark Code
Benchmark
GEO.9.4.1.1
The student will recognize and use ratios and proportions and apply their
properties.
GEO.9.4.1.2
GEO.9.4.1.3
GEO.9.4.1.4
The student will identify similar figures and use them to solve problems.
The student will identify and use similar triangles to solve problems.
The student will use the properties of similarity in right triangles to find
missing sides or angles.
GEO.9.4.1.5
The student will use proportional parts of triangles to solve problems and
divide a segment into congruent parts.
GEO.9.4.1.6
The student will recognize and use the proportional relationships of
corresponding perimeters, altitudes, angle bisectors, and medians of similar
triangles.
Standard 2: The student identifies, classifies, and applies theorems relating to triangles. The student
also applies congruence to different types and parts of triangles while identifying and using medians,
altitudes, angle bisectors, perpendicular bisectors. Indirect reasoning and indirect proofs will be used
to reach conclusions and solve problems.
Benchmark Code
Benchmark
GEO.9.4.2.1
The student will identify congruent figures.
GEO.9.4.2.2
The student will prove triangle congruence by Side-Side-Side , SideAngle-Side, Angle-Side-Angle and Angle-Angle-Side theorems.
GEO.9.4.2.3
The student will use congruent triangles to prove the CPCTC
(corresponding parts of congruent triangles are congruent).
GEO.9.4.2.4
The student will identify isosceles and equilateral triangles.
GEO.9.4.2.5
The student will prove congruence in right triangles.
GEO.9.4.2.6
The student will use corresponding parts of congruent triangles.
GEO.9.4.2.7
The student will identify and use medians, altitudes, angle bisectors, and
perpendicular bisectors in a triangle.
GEO.9.4.2.8
The student will use indirect reasoning and indirect proof to draw
conclusions.
Revised June 2011
GEO.9.4.2.9
The student will recognize and apply properties of inequalities to find the
measures of segments and angles.
GEO.9.4.2.10
The student will apply the Triangle Inequality Theorem to verify possible
sides of triangles.
Standard 3: The student investigates and uses the Pythagorean theorem and finds geometric mean
which will be used to solve triangles using the altitude to the hypotenuse.
Benchmark Code
Benchmark
GEO.9.4.3.1
The student will use paper folding to develop the Pythagorean Theorem.
GEO.9.4.3.2
The student will use tangent, sine and cosine ratios to find missing sides or
angles.
GEO.9.4.3.3
The student will use trigonometry to solve problems involving angles of
elevation or depression.
GEO.9.4.3.4
The student will apply properties of a right triangle to solve magnitude and
direction of vectors.
GEO.9.4.3.5
The student will use trigonometric functions to calculate area in figures.
Strand 5: Quadrilaterals
Standard 1: The student is introduced to various quadrilaterals and uses technology to investigate
some while employing the properties of parallelograms, rhombi, rectangles, squares and trapezoids to
solve problems.
Benchmark Code
Benchmark
GEO.9.5.1.1
The student will classify quadrilaterals.
GEO.9.5.1.2
The student will identify properties of parallelograms.
GEO.9.5.1.3
The student will prove that a quadrilateral is a parallelogram by analyzing
their unique properties.
GEO.9.5.1.4
The student will recognize and apply the properties of rectangles and
squares.
GEO.9.5.1.5
The student will recognize and apply the properties of rhombi and
trapezoids.
GEO.9.5.1.6
The student will place figures on a coordinate plane.
GEO.9.5.1.7
The student will write proofs using coordinate geometry.
Strand 6: Area
Standard 1: The student identifies and names polygons and investigates interior and exterior angle
measures of convex and regular polygons. The student also identifies types of tessellations.
Benchmark Code
Benchmark
GEO.9.6.1.1
The student will find the area of parallelograms and triangles.
GEO.9.6.1.2
The student will apply the Pythagorean theorem and its converse to find
area.
GEO.9.6.1.3
The student will apply the properties of special right triangles to find area
and missing sides.
Revised June 2011
GEO.9.6.1.4
The student will calculate the area of trapezoids, rhombi and kites.
GEO.9.6.1.5
The student will calculate the area of regular polygons.
GEO.9.6.1.6
The student will measure circles and arcs.
GEO.9.6.1.7
The student will find areas of circles and sectors.
GEO.9.6.1.8
The student will apply geometric probability to situational problems .
Strand 7: Three-Dimensional Geometry
Standard 1: The student recognizes and draws many three-dimensional figures and flattens these
figures to look at nets and surface area. The student determines surface area and volume of prisms,
cylinders, pyramids, cones and spheres.
Benchmark Code
Benchmark
GEO.9.7.1.1
The student will create cross sections and other slices of solids.
GEO.9.7.1.2
The student will use top, front, side, and corner views of three-dimensional
solids to make models and describe and draw cross sections and other
slices of three-dimensional figures.
GEO.9.7.1.3
The student will construct a tetrahedron kite.
GEO.9.7.1.4
The student will draw three-dimensional figures on isometric dot paper
and make two-dimensional nets.
GEO.9.7.1.5
GEO.9.7.1.6
GEO.9.7.1.7
GEO.9.7.1.8
GEO.9.7.1.9
GEO.9.7.1.10
GEO.9.7.1.11
GEO.9.7.1.12
GEO.9.7.1.13
The student will find the surface area of three-dimensional solids .
The student will find the lateral area and surface area of a right prism and a
right cylinder.
The student will find the lateral area and surface area of a regular pyramid
and a right circular cone.
The student will find the volume of a right prism and a right cylinder.
The student will compare the volumes of prisms and pyramids and the
volumes of cylinders and cones.
The student will find the volume of a pyramid and circular cone.
The student will recognize and define basic properties of spheres.
The student will find the surface area and the volume of a sphere.
The student will identify congruent or similar solids and state the
properties of congruent solids.
Strand 8: Circles
Standard 1: The student defines radius, diameter and circumference. The student uses major and
minor arcs and their relationships to central angles. The student develops theorems involving
inscribed angles and intercepted arcs using chords, secants, tangents and their properties.
Benchmark Code
Benchmark
GEO.9.8.1.1
The student will identify and use parts of circles.
GEO.9.8.1.2
The student will solve problems involving the circumference of a circle.
GEO.9.8.1.3
The student will recognize major arcs, minor arc, semicircles, and central
angles.
GEO.9.8.1.4
The student will find measures of arcs and central angles and solve
problems by making circle graphs.
Revised June 2011
GEO.9.8.1.5
The student will recognize and use relationships among arcs, chords, and
diameters.
GEO.9.8.1.6
The student will recognize and find measures of inscribed angles and
apply properties of inscribed figures.
The student will recognize tangents and use their properties.
The student will find the measures of angles formed by intersecting
secants and tangents in relation to intercepted arcs
GEO.9.8.1.7
GEO.9.8.1.8
GEO.9.8.1.9
The student will use the properties of chords, secants and tangents to solve
segment measure problems.
GEO.9.8.1.10
The student will write and use the equation of a circle in the coordinate
plane.
Strand 9: Tools of Algebra
Standard 1: The student evaluates and simplifies expressions, solves equations, solves and graphs
inequalities
Benchmark Code
Benchmark
A.9.9.1.1
The student will use the order of operations to evaluate expressions and use
formulas.
A.9.9.1.2
The student will determine the sets of numbers to which a number belongs.
A.9.9.1.3
The student will translate verbal expressions and sentences into Aebraic
expressions and equations.
A.9.9.1.4
The student will solve equations by using the properties of equalities.
A.9.9.1.5
The student will solve equations for a specific variable.
A.9.9.1.6
The student will solve equations containing absolute value and problems by
using a table.
A.9.9.1.7
The student will solve inequalities and graph the solution sets.
A.9.9.1.8
The student will solve compound inequalities using the properties of “and/or”.
A.9.9.1.9
The student will solve inequalities involving absolute value and graph the
solution.
Strand 10: Functions, Equations and Graphs
Standard 1: The student identifies different types of relations and functions, graphs relations and
functions on the coordinate plane, looks for patterns to solve problems, models real-world data using
scatter plots, and graphs inequalities on the coordinate plane.
Benchmark Code
Benchmark
A.9.10.1.1
The student will graph relations, state its domain and range, and determine
if it is a function.
A.9.10.1.2
The student will identify and graph linear equations.
A.9.10.1.3
The student will write linear equations in standard form.
A.9.10.1.4
The student will determine the intercepts of a line and use them to graph
an equation.
A.9.10.1.5
The student will determine the slope of a line and use slope and a point to
Revised June 2011
graph an equation.
A.9.10.1.6
The student will identify and use patterns points or linear equations to
make conclusions.
A.9.10.1.7
The student will write an equation of a line in slope-intercept form given
the slope and/or two points.
A.9.10.1.8
The student will write an equation of a line that is parallel or perpendicular
to the graph of a given equation.
A.9.10.1.9
The student will draw scatter plots to find and use prediction equations.
A.9.10.1.10
The student will draw graphs of inequalities with two variables.
Strand 11: Linear Systems
Standard 1: The student solves systems of equations in two or three variables, solves systems of
inequalities, uses linear programming to find maximum and minimum values of functions, and solves
problems by solving simpler problems.
Benchmark Code
Benchmark
A.9.11.1.1
The student will solve systems of equations by graphing.
A.9.11.1.2
The student will use the substitution and elimination methods to solve
system of equations.
A.9.11.1.3
The student will find the values of second-order determinants.
A.9.11.1.4
The student will solve system of equations by using Cramer’s rule.
A.9.11.1.5
The student will solve system of inequalities by graphing.
A.9.11.1.6
The student will find the maximum and minimum values of a function
over a region using linear programming techniques.
A.9.11.1.7
The student will apply Aebraic rules to solve word problem.
A.9.11.1.8
The student will solve problems involving maximum and minimum values
by using linear programming techniques.
A.9.11.1.9
The student will solve a system of three equations with three variables.
A.9.11.1.10
The student will determine the octant in which a point in space is located.
A.9.11.1.11
The student will graph linear equations in space and determine the
intercepts.
Revised June 2011