ESSENTIAL QUESTIONS

Directions

  • The following MUST be included in your essential questions document:
    1. Name
    2. Section of EQ
    3. Copy & Paste EQ's
    4. Under each EQ, state your answer in complete sentences.
      • In this class, a complete sentence refers to a sentence in which you can infer the question being asked and provide your response to the question.
    5. Leave a space between each question.


Chapter 1


1.1 ESSENTIAL QUESTIONS
  1. What are the three essential building blocks of geometry?
  2. What is the difference between a point, a line, and a plane?
  3. What are the basic construction tools?
  4. What is the difference between coplanar lines and skew lines?
  5. What is the difference between sketching a geometric figure, drawing a geometric figure, and constructing a geometric figure?
  6. What is the difference between duplicating a line segment and constructing a line segment?

1.2 ESSENTIAL QUESTIONS
  1. Where is the vertex of an angle?
  2. When can an angle be named using only a single capital letter?
  3. What is used to measure an angle and what is the unit of measure?
  4. Which scale should be used on a protractor when measuring an angle?
  5. What is the difference between an acute angle, an obtuse angle, a right angle, and a straight angle?
  6. What are congruent angles?
  7. What is an angle bisector?
  8. What is the difference between duplicating an angle and constructing an angle?

1.3 ESSENTIAL QUESTIONS
  1. What is the difference between a pair of supplementary and a pair of complementary angles?
  2. What determines perpendicularity?
  3. What is the difference between a bisector and a midpoint?
  4. In a diagram, how is a linear pair of angles recognized?
  5. In a diagram, how is a pair of vertical angles recognized?

1.4 ESSENTIAL QUESTIONS
  1. Describe a situation where you have used inductive reasoning.
  2. Describe a situation where you have used deductive reasoning.
  3. Describe the difference between inductive and deductive reasoning.

1.5 ESSENTIAL QUESTIONS
  1. What makes a statement a conditional statement?
  2. How is the truth value of a conditional statement determined?
  3. What is the difference between a postulate and a theorem?
  4. When is it appropriate to use the Linear Pair Postulate?
  5. When is it appropriate to use the Segment Addition Postulate?
  6. When is it appropriate to use the Angle Addition Postulate?

1.6 ESSENTIAL QUESTIONS
  1. What is the difference between the Addition Property of Equality and the Subtraction Property of Equality?
  2. What is the difference between the Identity Property and the Reflexive Property?
  3. What is the difference between the Substitution Property and the Transitive Property?
  4. What are four models of proof?
  5. If two angles are either supplements or complements of the same or congruent angles, what can be concluded?
  6. When are vertical angles congruent?

Chapter 2


2.1 ESSENTIAL QUESTIONS
  1. Describe all possible relationships between two lines. 2. What is the difference between alternate interior angles and alternate exterior angles?
  2. What do alternate interior angles and alternate exterior angles have in common?
  3. What is the difference between same-side interior angles and same-side exterior angles?
  4. What do same-side interior angles and same-side exterior angles have in common?

2.2 ESSENTIAL QUESTION
  1. What is the Corresponding Angle Postulate?

2.3 ESSENTIAL QUESTIONS
  1. If two parallel lines are cut by a transversal, which angle pairs are congruent?
  2. If two parallel lines are cut by a transversal, which angle pairs are supplementary?

2.4 ESSENTIAL QUESTIONS
  1. What needs to be done to a conditional statement to rewrite it as the converse?
  2. What is the difference between the Corresponding Angle Postulate and the Corresponding Angle Converse Postulate?
  3. What is the difference between the Alternate Interior Angle Theorem and the Alternate Interior Angle Converse Theorem?
  4. What is the same in all of the converse theorems?

2.5 ESSENTIAL QUESTIONS
  1. What is the difference between a triangle and a quadrilateral?
  2. What is the difference between a convex figure and a concave figure?
  3. What is a reflex angle?
  4. What is the difference between a regular polygon and an irregular polygon?
  5. Which polygon has five sides?
  6. How many sides are in a hexagon?
  7. What is a heptagon?
  8. Which polygon has eight sides?
  9. What is a nonagon?
  10. Which polygon has ten sides?

2.6 ESSENTIAL QUESTIONS
  1. What is the difference between an equilateral triangle and an equiangular triangle?
  2. Which triangles are used to classify triangles by the lengths of their sides?
  3. Which triangles are used to classify triangles by the measures of their angles?
  4. What is the difference between a rectangle and a square?
  5. What is the difference between a rhombus and a square?
  6. What is the difference between a parallelogram and a kite?
  7. What is the difference between a parallelogram and a trapezoid?
  8. What is the difference between an example and a counterexample?

Chapter 3


3.1 ESSENTIAL QUESTIONS

Chapter 4


4.1 ESSENTIAL QUESTIONS
  1. Explain the Triangle Sum Theorem.
  2. What happens to the length of a side opposite an interior angle of a triangle as the measure of the angle increases?
  3. Which angles in a triangle are considered remote interior angles?
  4. What is the relationship between the measure of an exterior angle of a triangle and the measure of the two remote interior angles

4.2 ESSENTIAL QUESTIONS
  1. What is a radical sign?
  2. How is a radical expression different from other algebraic expressions?
  3. Why is a fraction with a radical in the denominator not in simplest form?
  4. What is the difference between the Pythagorean Theorem and the Converse of the Pythagorean Theorem?
  5. When is the Pythagorean Theorem used?
  6. When is the Converse of the Pythagorean Theorem used?

4.3 ESSENTIAL QUESTIONS
  1. What is another name for a 45–45–90 triangle?
  2. How is the length of a leg used to calculate the length of the hypotenuse in a 45–45–90 triangle?
  3. How is the length of the hypotenuse used to calculate the length of a leg in a 45–45–90 triangle

4.4 ESSENTIAL QUESTIONS
  1. How is the length of the shorter leg used to calculate the length of the hypotenuse in a 30– 60– 90 triangle?
  2. How is the length of the shorter leg used to calculate the length of the longer leg in a 30– 60– 90 triangle?
  3. How is an equilateral triangle used to construct a 30– 60– 90 triangle?

4.5 ESSENTIAL QUESTIONS
  1. Using the measures of the interior angles of a triangle, how is the longest side located?
  2. Using the lengths of the sides of a triangle, how is the largest interior angle located?
  3. Using the measures of the interior angles of a triangle, how is the shortest side located?
  4. Using the lengths of the sides of a triangle, how is the smallest interior angle located?
  5. Why don’t the lengths of any three sides determine a triangle? (Explain the Triangle Inequality Theorem)

Chapter 5


5.1 ESSENTIAL QUESTIONS
  1. Can all numbers be expressed as ratios?
  2. Which numbers cannot be expressed as a ratio?
  3. What is an example of a number that cannot be expressed as a ratio?
  4. Can pi be expressed as a ratio?
  5. How do you calculate a ratio equivalent to 3/4?
  6. How many ratios are equivalent to 3/4?
  7. What is the difference between a ratio and a proportion?
  8. What is an example of a proportion that is not true?
  9. What operations are used to solve a proportion?

5.2 ESSENTIAL QUESTIONS
  1. What are similar polygons?
  2. What is the relationship between the ratio of side lengths of similar polygons and the ratio of areas of similar polygons?
  3. What is the relationship between the ratio of heights of similar polygons and the ratio of areas of similar polygons?
  4. What is the relationship between the ratio of side lengths of similar polygons and the ratio of perimeters of similar polygons?
  5. How is the scale model of a figure different from the actual figure?

5.3 ESSENTIAL QUESTIONS
  1. Are all equilateral triangles similar? Explain.
  2. Are all equiangular triangles similar? Explain.
  3. Are all right triangles similar? Explain.
  4. Are all isosceles triangles similar? Explain.
  5. Are all squares similar? Explain.
  6. Are all rectangles similar? Explain.

5.4 ESSENTIAL QUESTIONS
  1. What is an angle bisector?
  2. Describe the location of the adjacent sides of an angle in a triangle.
  3. Describe the location of the opposite side of an angle in a triangle.

5.5 ESSENTIAL QUESTIONS
  1. What is an altitude in a triangle?
  2. How many triangles are formed when an altitude to the hypotenuse of a right triangle is drawn?
  3. Can the geometric mean be used in any triangle?
  4. Why would someone use the geometric mean?

5.6 ESSENTIAL QUESTIONS
  1. What is direct measurement?
  2. What is indirect measurement?
  3. What is the difference between direct and indirect measurement?
  4. When is indirect measurement used?


Chapter 6


6.1 ESSENTIAL QUESTIONS
  1. What conjecture can be made about congruent triangles based on the corresponding sides?
  2. What conjecture can be made about congruent triangles based on the corresponding angles?
  3. What conjecture can be made about congruent triangles based on two corresponding sides and the included angle?
  4. What conjecture can be made about congruent triangles based on two corresponding angles and the included side?

6.2 ESSENTIAL QUESTIONS
  1. What is the SSS Congruence Theorem?
  2. What is the SAS Congruence Theorem?
  3. What is the ASA Congruence Theorem?
  4. What is the AAS Congruence Theorem?
  5. Why isn’t AAA a congruence Theorem?

6.3 ESSENTIAL QUESTIONS
  1. What triangle congruency theorem can be associated with the Leg-Leg Congruence Theorem?
  2. What triangle congruency theorem can be associated with the Hypotenuse-Angle Congruence Theorem?
  3. What triangle congruency theorem can be associated with the Leg-Angle Congruence Theorem?
  4. What triangle congruency theorem can be associated with the Hypotenuse-Leg Congruence Theorem?
  5. Why does the Hypotenuse-Leg Congruence Theorem work if Side-Side-Angle is not a congruence postulate?

6.4 ESSENTIAL QUESTIONS
  1. What is CPCTC?
  2. What are the prerequisites for using CPCTC?
  3. What is an isosceles triangle?
  4. If two sides of a triangle are congruent, what can be concluded?
  5. If two angles of a triangle are congruent, what can be concluded?

6.5 ESSENTIAL QUESTIONS
  1. What effect does the altitude to the base of an isosceles triangle have on the base?
  2. What effect does the altitude to the base of an isosceles triangle have on the vertex angle?
  3. What is true about the altitudes to the congruent sides of an isosceles triangle?
  4. What is true about the angle bisectors of the congruent sides of an isosceles triangle?

6.6 ESSENTIAL QUESTIONS
  1. What is a conditional statement?
  2. What is the difference between the converse of a conditional statement and the inverse of a conditional statement?
  3. What is the difference between the converse of a conditional statement and the contrapositive of a conditional statement?
  4. What is the difference between a direct proof and an indirect proof?
  5. What is the Hinge Theorem? 6. What is the Hinge Converse Theorem?


Chapter 7

Chapter 8


8.1 ESSENTIAL QUESTIONS8
  1. What is the difference between a square and a rectangle?
  2. What is the difference between the properties of the diagonals of a square and the properties of the diagonals of a rectangle?
  3. If the opposite sides of a quadrilateral are parallel, is the quadrilateral a square or a rectangle?
  4. If the diagonals of a quadrilateral are congruent, is the quadrilateral a square or a rectangle?

8.2 ESSENTIAL QUESTIONS
  1. What is the difference between a parallelogram and a rhombus?
  2. What is the difference between the properties of the diagonals of a parallelogram and the properties of the diagonals of a rhombus?
  3. If the opposite sides of a quadrilateral are parallel, is the quadrilateral a rhombus?
  4. If the diagonals of a quadrilateral are perpendicular, is the quadrilateral a square or a rhombus?

8.3 ESSENTIAL QUESTIONS
  1. What is the difference between a parallelogram and a kite?
  2. Do the diagonals of a kite bisect each other?
  3. If the opposite angles of a quadrilateral are congruent, do the opposite sides also have to be congruent? Explain.
  4. If the opposite sides of a quadrilateral are congruent, do the opposite angles also have to be congruent? Explain.
  5. Are the base angles of a trapezoid congruent?
  6. If the diagonals of a quadrilateral are perpendicular to each other, do they also bisect each other?
  7. What is the difference between a conditional statement and a biconditional statement?

8.4 ESSENTIAL QUESTIONS
  1. How do we calculate the sum of the measures of the interior angles of a 13-sided polygon?
  2. How do we determine the number of sides of a polygon when the sum of the measures of the interior angles of the polygon is 2700 degrees?
  3. How do we calculate the measure of each interior angle of a regular polygon with 12 sides?
  4. How do we determine the number of sides of a regular polygon, if the measure of each interior angle is 165.6 degrees?
  5. Calculate the sum of the measures of the interior angles of an 18-sided polygon.
  6. Determine the number of sides of a polygon when the sum of the measures of the interior angles of the polygon is 2160 degrees.
  7. Calculate the measure of each interior angle of a regular polygon with 30 sides.
  8. Determine the number of sides of a regular polygon if the measure of each interior angle is 172.8 degrees.

8.5 ESSENTIAL QUESTIONS
  1. How do we calculate the sum of the measures of the exterior angles of a 13-sided polygon?
  2. How do we determine the number of sides of a polygon when the sum of the measures of the exterior angles of the polygon is 360 degrees?
  3. How do we calculate the measure of each exterior angle of a regular polygon with 12 sides?
  4. How do we determine the number of sides of a regular polygon if the measure of each exterior angle is 14.4 degrees?
  5. Calculate the sum of the measures of the exterior angles of an 18-sided polygon.
  6. Calculate the measure of each exterior angle of a regular polygon with 30 sides.
  7. Determine the number of sides of a regular polygon if the measure of each exterior angle is 7.2 degrees.

8.6 ESSENTIAL QUESTIONS
  1. Which quadrilaterals are classified as parallelograms?
  2. Which quadrilaterals are not classified as parallelograms?
  3. Diagonals bisect each other is a property of which quadrilaterals?
  4. Diagonals are congruent is a property of which quadrilaterals?
  5. Diagonals are perpendicular is a property of which quadrilaterals?

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14