Download Geometry Essential Questions Module 1: • How do defined terms

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?