Radnor High School s2

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.

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 Classzone.com

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

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

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

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.

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,

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

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

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.

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,

Right Triangles and Trigonometry  Simplifying Square Roots  45º – 45º - 90º Triangles  30º – 60º - 90º Triangles  Tangent Ratio  Sine and Cosine Ratio  Solving Right Triangles

Circles  Parts of a Circle  Properties of Tangents  Arcs and Central Angles  Inscribed Angles

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