HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

Transcription

1 HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE/SUBJECT Geometry A KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS FOUNDATIONS FOR GEOMETRY REASONING PARALLEL & PERPENDICULAR LINES CONGRUENT TRIANGLES PROPERTIES OF TRIANGLES TRANSFORMATIONS Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

2 STANDARD CHAPTER LEARNING TARGETS EXAMPLE KEY CONCEPT Foundations for Geometry 1.1 G.CO.I Students will understand common language used in Geometry. Name a set of opposite rays. Apply basic facts about points, lines, and planes. Foundations for Geometry 1.2 G.CO.I Students will be able to calculate the distance/length of segments and understand the Segment Addition Postulate. Find AB. A = (0,3) & B = (5,1) Apply the distance formula, and work with the Segment Addition Postulate. Foundations for Geometry 1.3 G.CO.I Students will be able to name and classify angles. Classify BOA. Measure and classify angles and angle bisectors. Foundations for Geometry 1.4 G.CO.9 G.SRT.7 Identify adjacent, vertical, complementary, and supplementary angles. Find the complement of F. Find measures of pairs of angles.

3 STANDARD CHAPTER LEARNING TARGETS EXAMPLE KEY CONCEPT Foundations for Geometry 1.5 G.C.2.1 Students will be able to apply basic Geometry formulas. The circumference of a circle is 34 π cm. Find the radius. Apply formulas for perimeter, area, and circumferenc e. Foundations for Geometry 1.6 G.GPE.6.1 Students will be able to calculate the midpoints of segments and the distance between points on a coordinate plane. Find the midpoint between R = (-5, 1) & S = (7,0). Apply the midpoint and distance formula. CHAPTER 2.1 G.CO.1 G.CO.9 G.CO.10 Students will use inductive reasoning to identify patterns and make conjectures. Give an instance and a counterexample to: If n > -5, then n is positive. Apply instances, counterexampl es, conditional(s) and biconditionals. 2.2 G.CO.9 Students will explore Algebraic properties, definitions, postulates, and theorems and how they are used. Given: M is the midpoint of XY.. Justify XM MY. Identify properties of equality and congruence.

4 2.3 G.CO.9 Students will write two-column proofs. Prove given problems using deductive reasoning. 2.4 G.CO.9 Students will continue practicing writing two-column proofs. CHAPTER 3.1 G.GPE.5 A.CED.2 A.SSE.1 Students will find slope, write and graph equations for lines in point-slope form. Graph the equation y 3 = 1 (x + 2) 2 Slope and Point-slope form.

5 3.2 G.GPE.5 A.CED.2 A.SSE.1 Students will find slope, write and graph equations for lines in slope-intercept form. Write an equation in slope-intercept form for a line passing through (-3,6) and (-2,-8) Slopeintercept form. 3.3 G.GPE.5 Students will be able to state that parallel lines have the same slope. Students will be able to determine if lines are parallel using their slope. Determine whether the lines are parallel, perpendicular or neither by finding their slope. (-3, 2) and (4, -5) Find the slope of lines. Tell whether lines are parallel or perpendicular. Students will be able to write an equation for a line that is parallel to a given line that passes through a given point. Students will be able to determine if lines are perpendicular using their slope. Students will be able to write an equation for a line that is perpendicular to a given line that passes through a given point. Write an equation for a line in point-slope form that is parallel to y 3 = 7(x 1) that passes through the point (-4, 7). Write an equation in slope intercept form for a line perpendicular to y = 1 that passes 4 x 5 through the point (6, 2).

6 3.4 G.CO.9 Students will be able to identify transversals, corresponding angles, alternate internal angles, alternate exterior angles, same-side interior angles, and same-side exterior angles. Classify the angle pair. 1 & 5 Finding alternate interior, alternate exterior, corresponding, same-side interior, and same-side exterior angles. 3.5 G.CO.9 Students will be able to use alternate interior angles theorem and corresponding angles postulate to prove congruence (when a transversal crosses parallel lines). Find <ABD. Finding alternate interior, alternate exterior, corresponding, same-side interior, and same-side exterior angles.

7 3.6 G.CO.9 Students will be able to show angles relationships including AIA, AEA, CA, SSIA, and SSEA with proofs. Given : a // b, <1 <3 Prove : l // m Finding alternate interior, alternate exterior, corresponding, same-side interior, and same-side exterior angles in proofs. CHAPTER Congruent 4.1 G.CO.13 Students will be able to classify triangles by their angle measure. Students will be able to prove the measures of interior angles of a triangle are equal to 180. (Triangle Sum Theorem) In ABC, <A = 3x + 5, <B = 3x - 8, and <C = 4x - 9. Find <A. Finding angle measures of triangles.

8 Congruent 4.2 G.CO.10 Students will be able to prove the base angles of an isosceles triangle are congruent. (Isosceles Theorem) Find each side length. Find <F. Finding angle measures and side lengths in isosceles and equilateral triangles. Congruent 4.3 G.CO.7 Students will be able to identify if triangles are congruent by showing corresponding sides and angles are congruent, and they will be able to demonstrate that distance and angle measurement is preserved. ΔABC ΔDBC and <DBC. Find x Finding corresponding sides and angles in congruent triangles.

9 Congruent 4.4 G.CO.8 Students will be able to explain how SSS and SAS follow from the definition of congruence in terms of isometries and prove triangles are congruent. Students will be able to explain how ASA, AAS, and HL follow from the definition of congruence in terms of isometries and prove triangles are congruent. Explain what theorem shows the two triangles are congruent. Proving triangles are congruent using SSS, SAS, AAS, ASA, and HL. Congruent 4.5 G.SRT.5 Students will be able to use triangle congruence (SSS, SAS, ASA, AAS, and HL) to solve problems and prove relationships. Students will be able to use triangle congruence (ASA, AAS, and HL) to solve problems and prove relationships in figures. Given : K is the midpoint of HL and MJ Prove : ΔHJK ΔLMK Proving congruent pieces in congruent triangles using SSS, SAS, AAS, ASA, and HL.

10 Congruent 4.6 G.SRT.5 Students will be able to use triangle congruence (ASA, AAS, and HL) to solve problems and prove relationships in figures. Given: PR bisects < PQS and < QRS Prove : PQ = PS Proving congruent pieces in congruent triangles using SSS, SAS, AAS, ASA, and HL.

11 STANDARD CHAPTER LEARNING TARGETS EXAMPLE KEY CONCEPT Properties of 5.1 G.CO.9 G.C.3 Prove points on a perpendicular bisector are equidistant from end points. Define angle bisector and perpendicular bisector. Perpendicula r and Angle Bisectors Properties of 5.2 G.CO.10 Prove and use the triangle mid-segment formula. Find HI, GE and m<hgd. Triangle Midsegment Properties of 5.3 G.SRT.8 Estimate side length and angle measures based on the triangle inequality. Write the angles in order from smallest to largest. Indirect Proof and Inequalities in One Triangle

12 STANDARD CHAPTER LEARNING TARGETS EXAMPLE KEY CONCEPT Properties of 5.4 G.SRT.8 Use the Pythagorean Theorem to solve for an unknown side length of a right triangle. Find x. Pythagorean Theorem Properties of 5.5 G.SRT.6 Solve triangles problems. Find x. 45, 45, 90 Properties of 5.6 G.SRT.8 Solve triangles problems. Find x and y. 30, 60, 90

13 Transformations 12.1 G.CO.2 G.CO.3 G.CO.5 G.C0.6 Draw and identify reflections. Identify transformations that are rigid. Determine the coordinates after a transformation. Construct a reflection. Draw reflection & line of reflection. Congruency with rigid motions. Give the reflection of the point (-2,5) after it is reflected over the x axis. Reflections Transformations 12.2 G.CO.2 G.CO.3 G.CO.5 G.C0.6 Draw and identify translations Identify transformations that are rigid. Determine the coordinates after a transformation. Construct translation. Draw translation and the translation vector. Congruency with rigid motions Translate the point (2,5) along the vector (-2,6) Translations Transformations 12.3 G.CO.2 G.CO.3 G.CO.5 G.C0.6 Draw and identify rotations. Identify transformations that are rigid. Determine the coordinates after a - transformation. Construction rotation. Draw rotation and find the center of the rotation. Congruency with rigid motions Rotate the point (02,5) 90 degrees clockwise. Rotations Transformations 12.4 G.CO.2 G.CO.5 G.C0.6 Determine the coordinates after a transformation. Draw composition of transformations. Congruency with rigid motions Translate the point (-2,3) along the vector (5, 4) and then reflect it over the y axis. Composition of Transformations

14 Transformations 12.5 G.CO.2 Calculate the lines of symmetry and degree of rotational symmetry. Transformations 12.6 G.CO.2 Identify transformations that are not rigid. How many lines of symmetry in a regular pentagon? Find the image of the point (2,5) after a dilation of magnitude 3. Symmetry Dilations