Radnor High School - RTSD



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. |

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|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, |

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|TEXTS |

|Geometry; McDougal Littell Publishing Company |

|Activities, Assignments, & Assessments |

|ACTIVITIES |

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|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 |

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|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. |

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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: |

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|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 |

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|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 |

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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 |

| 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 |

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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: |

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|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 |

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|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 |

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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 |

| 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 |

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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: |

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|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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