Radnor High School - Radnor Township School District
Radnor High School
Course Syllabus
Geometry
0426
Credits: 1 Grades: 9-12
Weighted: no Prerequisite: Algebra 1
Length: year 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. |
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|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. |
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|Keystone Connections: |
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|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. |
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|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 |
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|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 |
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| |
|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 |
| |
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 |
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|Media, Technology, Web Resources |
| |
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 |
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|Similarity |
|Ratio and Proportion |
|Similar Polygons |
|Showing Triangles are Similar: AA |
|Showing Triangles are Similar: SSS and SAS |
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|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 |
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|Media, Technology, Web Resources |
| |
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 |
|45º – 45º - 90º Triangles |
|30º – 60º - 90º Triangles |
|Tangent Ratio |
|Sine and Cosine Ratio |
|Solving Right Triangles |
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|Circles |
|Parts of a Circle |
|Properties of Tangents |
|Arcs and Central Angles |
|Inscribed Angles |
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|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 |
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|Media, Technology, Web Resources |
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