Unit 5: Polygons and Quadrilaterals Scale for Unit 5 4 Through independent work beyond what was taught in class, students could (examples include, but are not limited to): - Research a unique building in their community and describe the shape of the building s faces and the properties of those shapes. - Use properties of polygons to identify challenges that architects experience when creating a building. 3 The students will: - Prove theorems about parallelograms; use theorems about parallelograms to solve problems. - Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). - Use coordinates to prove simple geometric theorems algebraically. - Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. 2 The students will: - Determine the meaning of symbols, key terms, and other geometry specific words. - Classify parallelograms. - Recall how to construct lines, angles, segments, and circles, and Slope, Distance, and Midpoint Formulas. - Understand the process of substituting values into a given equation and simplify. - Recall the definition of the perimeter of a polygon. - Comprehend properties of triangles, parallel lines, and perpendicular lines. 1 The student will be able to correctly use the following vocabulary: polygon, parallelogram, perimeter, triangle, rectangle, kite, base, and coordinates. Ranking: Date Level Notes: (what you didn t understand from the chapter and want to work on) Page 1 of 28
Sample Problem Scale: Level 4 Level 3 Level 2 Level 1 Page 2 of 28
BELLWORK: Date: Date: Date: Date: Page 3 of 28
BELLWORK: Date: Date: Date: Date: Page 4 of 28
Section 6-1 The Polygon Angle-Sum Theorems Page 5 of 28
EXAMPLES: Find the sum of the interior angles of each polygon. Find the missing angle measures. Find the measure of one exterior angle of each regular polygon. Find the value of each variable. The car at each vertex of a Ferris wheel holds a maximum of five people. The sum of the interior angle measures of the Ferris wheel is 7740. What is the maximum number of people the Ferris wheel can hold? A rectangle and square have equal areas. The rectangle has a length of 9 cm and a width of 4 cm. What is the perimeter of the square? Page 6 of 28
Section 6-2 Properties of Parallelograms Page 7 of 28
Examples: Find the value of x in the parallelogram. In the figure, TU = UV. Find each length. Find the measure of the numbered angles in each parallelogram. NM = QR = LN = QS = Page 8 of 28
Section 6-3 Proving that a Quadrilateral is a Parallelogram Page 9 of 28
EXAMPLES: Is there enough information to prove that ABCD is a parallelogram? Explain. Page 10 of 28
Section 6-4 Properties of Rhombuses, Rectangles, and Squares Page 11 of 28
Find the measure of the numbered angles in each rhombus. Page 12 of 28
Section 6-5 Conditions for Rhombuses, Rectangles, and Squares Page 13 of 28
EXAMPLES: Page 14 of 28
Section 6-6 Trapezoids and Kites Page 15 of 28
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Parallelogram Rhombus Rectangle Square Isosceles Trapezoid Kite 1 Set of Opposite Sides are Parallel 2 Sets of Opposite Sides are Parallel Opposite Sides are Congruent All 4 Sides are Congruent Opposite Angles are Congruent 4 Right Angles Base Angles are Congruent Consecutive Angles are Supplementary Diagonals are Congruent Diagonals are Perpendicular Diagonals Bisect Opposite Angles Diagonals Bisect Each Other Page 18 of 28
MIDUNIT REVIEW Page 19 of 28
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Section 6-7 Polygons in the Coordinate Plane Page 21 of 28
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Section 6-8 Applying Coordinate Geometry Page 23 of 28
Section 6-9 Proofs Using Coordinate Geometry Complete the following Coordinate Proofs (Proofs Using Information from a Coordinate Plane) Page 24 of 28
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UNIT 5 REVIEW: Page 26 of 28
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