Geometry Ch 3 - Parallel and Perpendicular Lines

Question 1

What is a Transversal?

Answer 1

A line that intersects two coplanar lines at two distinct points.

Example: The diagram shows the eight angles formed by a transveral t and two lines l and m.

Question 2

What are Alternate Interior Angles?

Answer 2

Question 3

What are Same Side Interior Angles?

Answer 3

Question 4

What are Corresponding Angles?

Answer 4

Question 5

What is the Corresponding Angles Postulate?

Answer 5

Question 6

What is the Alternate Interior Angles Theorem?

Answer 6

Question 7

What is the Same-Side Interior Angles Theorem?

Answer 7

Question 8

What is the Alternate Exterior Angles Theorem?

Answer 8

Question 9

What is the Same-Side Exterior Angles Theorem?

Answer 9

Question 10

What is the Converse of the Corresponding Angles Postulate?

Answer 10

Question 11

What is the Converse of the Alternate Interior Angles Theorem?

Answer 11

Question 12

What is the Converse of the Same-Side Interior Angles Theorem?

Answer 12

Question 13

What is the Converse of the Alternate Exterior Angles Theorem?

Answer 13

Question 14

If two lines are parallel to the same line, then…

Answer 14

they are parallel to each other.

Question 15

In a plane, if two lines are perpendicular to the same line, then…

Answer 15

they are perpendicular to each other.

Question 16

What is the Triangle Angle-Sum Theorem?

Answer 16

The sum of the measures of the angles of a triangle is 180.

Question 17

What is an Equiangular Triangle?

Answer 17

A triangle with all angles congruent.

Question 18

What is an Acute Triangle?

Answer 18

A triangle with all angles acute.

Question 19

What is a Right Triangle?

Answer 19

A triangle with one right angle.

Question 20

What is an Obtuse Triangle?

Answer 20

A triangle with one obtuse angle.

Question 21

What is an Equilateral Triangle?

Answer 21

A triangle with all sides congruent.

Question 22

What is an Isosceles Triangle?

Answer 22

A triangle with at least two sides congruent.

Question 23

What is a Scalene Triangle?

Answer 23

A triangle with no sides congruent.

Question 24

What is the Exterior and Interior Angles of a Polygon?

Answer 24

Question 25

What is the Triangle Exterior Angle Theorem?

Answer 25

Question 26

What is a Great Circle?

Answer 26

The intersection of a sphere and a plane that contains the center of the sphere.

Question 27

What is Euclid's Parallel Postulate?

Answer 27

Through a point not on a line, there is one and only one line parallel to the given line.

Question 28

What is the Spherical Parallel Postulate?

Answer 28

Through a point not on a line, there is no line parallel to the given line.

Question 29

What is a Polygon?

Answer 29

A closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear.

Question 30

What is a Convex Polygon?

Answer 30

A polygon having no diagonal with points outside the polygon.

Question 31

What is a Concave Polygon?

Answer 31

A polygon having at least one diagonal with points outside the polygon.

Question 32

What is the Polygon Angle-Sum Theorem?

Answer 32

The sum of the measures of the angles of an *n*-gon is (*n* - 2)180. Note: By dividing a polygon with n sides into n - 2 triangles, you can show that the sume of the measures of the angles of any polygon is a multiple of 180.

Question 33

What is the Polygon Exterior Angle-Sum Theorem?

Answer 33

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

Question 34

What is an Equilateral Polygon?

Answer 34

A polygon having all sides congruent.

Question 35

What is an Equiangular Polygon?

Answer 35

A polygon having all angles congruent.

Question 36

What is a Regular Polygon?

Answer 36

A polygon that is both equilateral and equiangular.

Question 37

What is the Slope of a line?

Answer 37

The ratio of the vertical change (rise) to the horizontal change (run) between any two points (x₁, y₁) and (x₂, y₂) of the line. Equation: Slope = Vertcal Change / Horizontal Change = rise / run = (y₂ - y₁) / (x₂ - x₁) The slope of a line indicates the steepness of the line and whether it rises or falls from left to right.

Question 38

What is the Slope-Intercept Form of a linear equation?

Answer 38

*y = mx + b*, where *m* is the slope of the line, and b is the *y*-intercept.

Question 39

What is the Standard Form of Linear Equation?

Answer 39

*Ax + By = C*, where *A*, *B* and *C* are real numbers, *A* and *B* are not both zero. Note: To graph an equation written in standard form, you can readily find two points for the graph by finding the *x-* and *y-*intercepts. See example.

Question 40

How do you convert a linear equation from Standard to Slope Intercept form?

Answer 40

Solve for y

Question 41

What is the Point-Slope Form for a Linear Equation?

Answer 41

For a nonvertical line through point (*x₁, y₁*) with slope m; *y - y₁ = m(x - x₁)*