Understanding Lines and Tangents

What are the different types of lines?

• Solid, Broken, Faded

• Thick, Thin, Dotted

• Straight, Curved, Horizontal, Vertical, Diagonal, Parallel, Perpendicular

• Circular, Elliptical, Triangular

Define a tangent line in relation to a circle.

• A tangent line is a line that touches a circle at exactly one point.

• A tangent line is a line that runs parallel to the circle.

• A tangent line intersects a circle at two points.

• A tangent line is a line that passes through the center of the circle.

How do you identify parallel lines?

• Parallel lines always form a right angle with each other.

• Parallel lines can be identified by their varying lengths.

• Parallel lines have the same slope and never intersect.

• Parallel lines have different slopes and intersect at one point.

Draw a line segment and label its endpoints.

• Line segment CD with endpoints C and D.

• Line segment XY with endpoints X and Y.

• Line segment PQ with endpoints P and Q.

• Line segment AB with endpoints A and B.

What is the difference between a ray and a line?

• A ray is a straight path with two endpoints; a line has one endpoint.

• A ray has a starting point and extends infinitely in one direction; a line extends infinitely in both directions.

• A ray extends infinitely in both directions; a line has a starting point.

• A ray is shorter than a line and can be measured; a line cannot be measured.

Explain how to draw a tangent line to a circle.

• A tangent line is drawn parallel to the diameter of the circle.

• A tangent line to a circle is drawn perpendicular to the radius at the point of tangency.

• A tangent line is drawn at the center of the circle.

• A tangent line intersects the circle at two points.

Identify the characteristics of intersecting lines.

• Intersecting lines have the same slope and never meet.

• Intersecting lines cross at multiple points.

• Intersecting lines cross at one point and have different slopes.

• Intersecting lines run parallel to each other.

What is the angle formed by two perpendicular lines?

• 180 degrees

• 30 degrees

• 45 degrees

• 90 degrees

How can you determine if two lines are parallel?

• Two lines are parallel if their slopes are equal.

• Two lines are parallel if they are both vertical.

• Two lines are parallel if they intersect at one point.

• Two lines are parallel if they have different slopes.

Provide an example of where tangent lines are used in real life.

• In vehicle dynamics to analyze trajectories.

• In sports to measure the speed of a ball during a game.

• In architecture to calculate the height of buildings.

• In cooking to determine the perfect angle for slicing.