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Radnor High School
Course Syllabus
Geometry
0426
Credits: 1
Weighted: no
Length: year
Grades: 9-12
Prerequisite: Algebra 1
Format: meets daily
Overall Description of Course
Geometry is an Academic level course.
Academic level courses will feature a slower pace with moderate workload and the highest
degree of teacher‐guidance to assist in the mastery of the material. These courses will cover
material necessary to prepare students for the PSSA tests and Keystone Exams as well as prepare
the student to take the SAT test if post secondary education is desired; however, some
independent math remediation may be necessary.
This course will cover the basic concepts of geometry at a moderate pace and an appropriate
difficulty level. Topics will include the definitions and properties of geometric shapes. The
concepts of congruence and similarity will be applied to appropriate figures and problem solving
situations. Perimeter, area, and volume formulas will be used for various geometric shapes.
Pythagorean Theorem and the right triangle trigonometric ratios will be introduced. Throughout
the course, algebra skills will be reviewed and reinforced through applications of geometric
concepts. This course is designed to help students meet the Pennsylvania State Standards in
mathematics.
Marking Period One
Common Core Standards
G.CO.1. Know precise definitions of angle, perpendicular line, parallel line, and line segment, based on the
undefined notions of point, line, distance along a line.
G-CO.9. Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
G-GPE.5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given
point).
G-GPE.6. Find the point on a directed line segment between two given points that partitions the segment in a
given ratio.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills:
 Name and identify points, lines and planes and their intersections.
 Classify collinear points and coplanar points and lines.
 Use segment addition postulate.
 Find the distance between two points on a number line.
 Name and classify angles.
 Use the angle addition postulate.
 Bisect a segment.
 Find the coordinates of a midpoint of a segment.
 Bisect an angle.
 Identify vertical angles, linear pair, complementary and supplementary angles.
 Recognize and analyze conditional statements and write their converses.
 Recognize and use bi-conditional statements for definitions.
 Identify relationships between lines.
 Identify angles formed by coplanar lines intersected by a transversal
 Use theorem about perpendicular lines.
 Find congruent angles formed when a transversal cuts parallel lines.
 Determine if two lines are parallel.
 Compute slope of a line.
 Write the equation of a line in point slope form.
 Write the equation of parallel and perpendicular lines.
Materials & Texts
MATERIALS
 Scientific calculator,
TEXTS
 Geometry; McDougal Littell Publishing Company
Activities, Assignments, & Assessments
ACTIVITIES
Basics of Geometry
 Points, Lines, and Planes
 Sketching Intersections
 Segments and Their Measures
 Angles and Their Measures
Segments and Angles
 Segment Bisectors
 Angle Bisectors
 Complementary and Supplementary Angles
 Vertical Angles
 If-Then Statements and Deductive Reasoning
 Properties of Equality and Congruence
Parallel and Perpendicular Lines
 Relationships Between Lines
 Theorems About Perpendicular Lines
 Angles Formed by Transversals
 Parallel Lines and Transversals
 Showing Lines are Parallel
 Parallel & Perpendicular Postulate
 Finding Slope & Writing Equations of Lines Using Slope-Intercept and Point-Slope
 Determine if Lines are Parallel, Perpendicular, or Neither
 Write Equations of Lines Parallel or Perpendicular
ASSIGNMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics
Department page of Radnor High School’s web site.
ASSESSMENTS
Grades will be based on quizzes and tests. In addition, teachers may use homework, group activities,
and/or projects for grading purposes. All students will take departmental midyear and final exams.
The Radnor High School grading system and scale will be used to determine letter grades.
Terminology
Point, line, plane, postulate, collinear points, coplanar, segment, endpoint, ray, intersect, coordinate,
distance, length, congruent, angle, sides, vertex, degrees, acute, right, obtuse, straight angle, midpoint,
segment bisector, angle bisector, complementary angles, complement of an angle, supplementary angles,
supplement of an angle, theorem, adjacent angles, vertical angles, linear pair, if-then statements,
hypothesis, conclusion, bi-conditional, parallel, perpendicular, skew lines, transversal, corresponding
angles, alternate interior angles, alternate exterior angles, same-side interior, converse.
Homework: All assignment Sheets for the entire course can be found on the math
department website.
Media, Technology, Web Resources
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Marking Period Two
Common Core Standards
G-CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given
rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to
decide if they are congruent.
G-CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if
and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G-CO.8. Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of
congruence in terms of rigid motions.
G-CO.10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to
180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle
is parallel to the third side and half the length; the medians of a triangle meet at a point.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills:
 Classify triangles by their sides and angles.
 Find angle measures in triangles.
 Use properties of isosceles and equilateral triangles.
 Use the Pythagorean Theorem and its converse.
 Use the distance formula.
 Indentify the medians and centroid of a triangle.
 Use Triangle Inequality Theorem.
 Rank triangle side or angles using their opposites’ measures.
 Identify congruent figures and corresponding parts.
 Prove triangles are congruent using SSS, SAS, ASA, AAS and HL.
 Use CPCTC to find missing measures of angles or sides.
 Use properties of perpendicular bisector of segments and angle bisectors
Materials & Texts
MATERIALS
 Scientific calculator,
TEXTS
 Geometry; McDougal Littell Publishing Company
Activities, Assignments, & Assessments
ACTIVITIES
Triangle Relationships
 Classifying Triangles
 Angle Measures of Triangles
 Isosceles and Equilateral Triangles
 The Pythagorean Theorem and the Distance Formula
 The Converse of the Pythagorean Theorem
 Medians of a Triangle
 Triangle Inequalities
Congruent Triangles
 Congruence and Triangles
 Using Congruence Postulates: SSS and SAS
 Using Congruence Postulates: ASA and AAS
 Hypotenuse-Leg Congruence Theorem: HL
 Using Congruent Triangles
 Angle Bisectors and Perpendicular Bisectors
ASSIGNMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics
Department page of Radnor High School’s web site.
ASSESSMENTS
Grades will be based on quizzes and tests. In addition, teachers may use homework, group activities,
and/or projects for grading purposes. All students will take departmental midyear and final exams.
The Radnor High School grading system and scale will be used to determine letter grades.
Terminology
Triangle, equilateral triangle, isosceles triangle, scalene triangle, equiangular triangle, acute triangle,
right triangle, obtuse triangle, vertex, interior angle, exterior angle, legs of an isosceles triangle , base of
an isosceles triangle, base angles of an isosceles triangle, legs of an isosceles triangle, legs of a right
triangle, hypotenuse, Pythagorean theorem, distance formula, median of a triangle, centroid,
corresponding parts, congruent figures, distance from a point to a line, perpendicular bisector
Media, Technology, Web Resources
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Marking Period Three
Common Core Standards
G-SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if
they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality
of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G-SRT.3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be
similar.
G-SRT.4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides
the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in
geometric figures.
G-CO.11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite
angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills:
 Identify, name and describe polygons
 Use the sum of the measures of the interior angles of a quadrilateral
 Use properties of parallelograms
 Show that a quadrilateral is a parallelogram
 Use properties of rhombi, rectangles and squares including properties of diagonals
 Use properties of trapezoids and isosceles trapezoids
 Identify special types of quadrilaterals based on limited information
 Use ratios and proportions
 Identify and use similar polygons
 Use the AA, SSS, and SAS similarity postulates
 Use the triangle proportionality theorem and its converse
 Find the measures of interior and exterior angles of a polygon
 Find the circumference of a circle
 Find the area of a circle and area of a sector
 Find the area of rectangles, parallelograms, squares, triangles, trapezoids and rhombi
Materials & Texts
MATERIALS
 Scientific calculator,
TEXTS
 Geometry; McDougal Littell Publishing Company
Activities, Assignments, & Assessments
ACTIVITIES
Quadrilaterals
 Polygons
 Properties of Parallelograms
 Showing Quadrilaterals are Parallelograms
 Rhombuses, Rectangles, and Squares
 Trapezoids
 Reasoning About Special Quadrilaterals
Similarity
 Ratio and Proportion
 Similar Polygons
 Showing Triangles are Similar: AA
 Showing Triangles are Similar: SSS and SAS
Polygons and Area
 Classifying Polygons
 Angles in Polygons
 Area of Squares and Rectangles
 Area of Triangles
 Area of Parallelograms
 Area of Trapezoids
 Circumference and Area of Circles
ASSIGNMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics
Department page of Radnor High School’s web site.
ASSESSMENTS
Grades will be based on quizzes and tests. In addition, teachers may use homework, group activities,
and/or projects for grading purposes. All students will take departmental midyear and final exams.
The Radnor High School grading system and scale will be used to determine letter grades.
Terminology
Polygon, side of a polygon, vertex of a polygon, diagonal of a polygon, parallelogram, rhombus,
rectangle, square, trapezoid, bases of a trapezoid, legs of a trapezoid, base angles of a trapezoid, isosceles
trapezoid, midsegment of a trapezoid, ratio of a to b, proportion, proportion, means of a proportion,
extremes of a proportion, similar polygons, scale factor, midsegment of a triangle, convex, concave,
equilateral, equiangular, regular, area, height of a triangle, base of a triangle, base of a parallelogram,
height of a parallelogram, height of a trapezoid, circle, center of a circle, radius, diameter, circumference,
central angle, sector
Media, Technology, Web Resources
Classzone.com
Marking Period Four
Common Core Standards
G-SRT.6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle,
leading to definitions of trigonometric ratios for acute angles.
G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles.
G-SRT.8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
G-C.2. Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship
between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the
radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G-C.5. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the
radius; derive the formula for the area of a sector.
Keystone Connections:
Student Objectives:
At the end of this quarter, student should be able to successfully complete the following skills:
 Simplify square roots
 Find the side lengths of 45º – 45º - 90º Triangles and 30º – 60º - 90º Triangles
 Find sine, cosine, and tangent ratios of an acute angle of a right triangle
 Solve a right triangle
 Identify segments and lines related to circles
 Use properties of tangents and arcs of circles
 Use properties of inscribed angles of circles
 Calculate the arc length
Materials & Texts
MATERIALS
 Scientific calculator,
TEXTS
 Geometry; McDougal Littell Publishing Company
Activities, Assignments, & Assessments
ACTIVITIES
Right Triangles and Trigonometry
 Simplifying Square Roots
Circles
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45º – 45º - 90º Triangles
30º – 60º - 90º Triangles
Tangent Ratio
Sine and Cosine Ratio
Solving Right Triangles
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Parts of a Circle
Properties of Tangents
Arcs and Central Angles
Inscribed Angles
ASSIGNMENTS
Assignment sheets will be distributed periodically throughout the school year. Homework will be
assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics
Department page of Radnor High School’s web site.
ASSESSMENTS
Grades will be based on quizzes and tests. In addition, teachers may use homework, group activities,
and/or projects for grading purposes. All students will take departmental midyear and final exams.
The Radnor High School grading system and scale will be used to determine letter grades.
Terminology
Radical, 45º – 45º - 90º Triangles, 30º – 60º - 90º Triangles, trigonometric ratio, leg opposite an angle,
leg adjacent to an angle, tangent, sine, cosine, solve a right triangle, inverse tangent, inverse sine, inverse
cosine, chord, secant, tangent, minor arc, major arc, arc length, inscribed angle intercepted arc
Media, Technology, Web Resources
Classzone.com