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Geometry Essential Questions Module 1: How do defined terms and undefined terms relate to each other? Provide an example of each and the definition and why it is defined or undefined. Explain how you construct one of the following figures: congruent segments, segment bisectors, angles, angle bisectors, parallel lines, or perpendicular lines using a compass and straightedge or technology? (Hint – page 12 of Lesson 1.02) How do you construct a regular polygon inside of a circle using technology or compass/straightedge? (You can use a regular hexagon, square, equilateral triangle.) (Hint – page 5 of lesson 1.03) Module 2: What are the similarities and differences between translations, reflections, and rotations? Provide an example of how to draw transformed figures that are translated, reflected, and rotated. How do you connect the ideas of congruency and rigid motion and how do you prove congruency? Module 3: Explain how to prove one of the following theorems: Vertical Angles, Corresponding Angles or Alternate Interior Angles. What type of information do you need to prove that two triangles are congruent? Explain how to prove one of the following properties of parallelograms: opposite sides are congruent, opposite angles are congruent, diagonals bisect each other. Module 4: How do you dilate a figure on the coordinate plane and determine its scale factor? How do you determine if polygons are similar? How do you determine if two triangles are similar? Module 5: What properties or characteristics of similar triangles could be used to prove the Pythagorean Theorem? How do you prove that a line parallel to one side of a triangle divides the other two sides proportionally and converse (Triangle Proportionality Theorem)? Explain how to prove one of the following: In an isosceles trapezoid, how do you prove the base angles are congruent or in a kite the long diagonal of a kite is a perpendicular bisector to the short diagonal, how can you prove that adjacent sides are congruent in a kite? Module 6: How do you use the distance formula and slope formula to classify a quadrilaterals and triangles? How do you write an equation of a line so that it is parallel or perpendicular to a given point and a given line? How do you use coordinates to find the perimeter and area of polygons? Module 7: How do similar right triangles lead to the definitions of the trigonometric ratios? What is the relationship between the sine and cosine of complementary angles and why is this relationship true? How do you use trigonometric ratios to solve for a missing side or angle of a right triangle? Module 8: How are the formulas for the volume of a cylinder, pyramid, and cone derived? How do changes in dimensions affect the volume of common geometric solids? What does a two-dimensional cross-section of three-dimensional object look like and how is that related to Cavalieri’s Principle? Module 9: How do you prove two circles are similar? What is the relationship among inscribed angles, radii, and chords? Central, circumscribed and inscribed angles? Inscribed angles and diameter? Radii and tangents? How do you construct the inscribed and circumscribed circles of a triangle and what do you know about opposite angles of inscribed quadrilaterals?