Geometry Syllabus

2nd  Nine Weeks (2nd  Quarter)

Standard

 G.CO.B.8 Understand congruence in terms of rigid motions G.CO.C.11 Prove geometric theorems G.SRT.A.1; 2; 3 Understand similarity in terms of similarity transformations G.SRT.B.4; 5 Prove theorems involving similarity G.MG.A.1, 2 Apply geometric concepts in modeling situations.   The following practice standards will be used throughout the quarter: 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Objectives

(Student Friendly “I can” statements)

 The learner will…   - Explain how the criteria for triangle congruence (ASA, SAS,AAS, and SSS) follow from the definition of congruence in terms of rigid motions. (I can use the definition of congruence, based on rigid motion, to explain the triangle congruence criteria (ASA, SAS SSS))   -Prove theorems about parallelograms. Proving includes, but is not limited to, completing partial proofs; constructing two-column or paragraph proofs; using transformations to prove theorems; analyzing proofs; and critiquing completed proofs. Theorems include but are not limited to: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. (I can define and describe the following quadrilaterals: all parallelograms, all trapezoids, and kites. I can prove the opposite sides of a parallelogram are congruent. I can prove the opposite angles of a parallelogram are congruent. I can prove the diagonals of a parallelogram bisect each other. I can prove rectangles are parallelograms with congruent diagonals.)   - Verify informally the properties of dilations given by a center and a scale factor. Properties include but are not limited to: a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center of the dilation unchanged; the dilation of a line segment is longer or shorter in the ratio given by the scale factor. (I can define dilation. I can perform a dilation with a given center and scale factor on a figure in the coordinate plane. I can verify that when a side passes through the center of dilation, the side and its image lie on the same line. I can verify that corresponding sides of the pre-image and images are parallel and proportional.)   - 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. (I can define similarity as a composition of rigid motions followed by dilations in which angle measure is preserved and side length is proportional. I can identify corresponding sides and corresponding angles of similar triangles. I can determine scale factor between two similar figures and use the scale factor to solve problems. I can demonstrate that corresponding angles are congruent and corresponding sides are proportional in a pair of similar triangles.)   - Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. (I can determine that two figures are similar by verifying that angle measure is preserved and corresponding sides are proportional. I can show and explain that when two angles measures (AA) are known, the third angle measure is also known. (Third Angle Theorem) I can use triangle similarity theorems such as AA, SSS and SAS to prove two triangles are similar.) -Prove theorems about similar triangles. (I can prove a line parallel to one side of a triangle divides the other two proportionally. I can prove if a line divides two sides of a triangle proportionally; then it is parallel to the third side.)   - Use congruence and similarity criteria for triangles to solve problems and to justify relationships in geometric figures.   -Use geometric shapes, their measures, and their properties to describe objects. (I can use geometric shapes, their measures and their properties to describe objects.)   -Apply geometric methods to solve real-world problems. (I can apply geometric methods to solve design problems.)   Honors Addendum Embed the Honors Addendum within the regular Scope & Sequence. -Relationships Within Triangles. Construct the points of concurrency within a triangle and solve problems using the properties of the centroid, orthocenter, incenter, and circumcenter. (I can distinguish among altitudes, angle bisectors, perpendicular bisectors, medians and midsegments in triangles and use their properties to solve problems. I can distinguish among the centroid, orthocenter, incenter, and circumcenter in a triangle and use the properties of each to solve problems. I can construct special segments in triangles using a compass and a straight edge or patty paper. I can use points of concurrency to construct and make conjectures about the Euler Line.)

Topics

•  What makes triangles congruent ASA triangle congruence SAS triangle congruence SSS triangle congruence Justifying constructions AAS triangle congruence HL triangle congruence Interior and exterior angles Isosceles and equilateral triangles Triangle inequalities Perpendicular bisectors of triangles Angle bisectors of triangles Medians and altitudes of triangles Midsegments of triangles Properties of parallelograms Conditions for parallelograms Properties of rectangles, rhombuses and squares Conditions for rectangles, rhombuses and squares

Assessments

Pre-assessments; ongoing module assessments to periodically measure understanding; unit assessment

 Instructional Materials Computer, manipulatives, geometers sketch pad, projection screen, laser printer, KUTA software, HRM AGA resources, dry erase boards, HRM textbook, protractor, compass, ruler, Promethean Board and clickers Field Trip/s NONE