Triangle Properties and Transformations

The video tutorial covers four practice problems from lesson two, focusing on geometric transformations. The first problem explores dilation with a point on a circle, examining scale factors and their reciprocals. The second problem involves dilating a triangle using different scale factors, highlighting the congruence of angles. The third problem demonstrates rigid transformations, including reflection and rotation, to map images. The final problem constructs a triangle from angles on a line, emphasizing the sum of angles in a triangle.

What is the center of dilation in a geometric transformation?

• The midpoint of the line segment

• The vertex of a triangle

• The intersection of two lines

• The point from which all points are expanded or contracted

If a point is dilated with a scale factor of 5/4, what happens to its distance from the center of dilation?

• It becomes zero

• It increases

• It decreases

• It remains the same

When a triangle is dilated with a scale factor of 2, what happens to its side lengths?

• They are halved

• They remain the same

• They are tripled

• They are doubled

What is the result of scaling a triangle with a factor of 1/2?

• The triangle becomes larger

• The triangle becomes smaller

• The triangle remains the same size

• The triangle disappears

How does scaling affect the angles of a triangle?

• Angles become larger

• Angles become smaller

• Angles remain congruent

• Angles disappear

Which transformation involves flipping a figure over a line?

• Reflection

• Rotation

• Translation

• Dilation

What is the line of reflection in a geometric transformation?

• A line that is parallel to the figure

• A line that is perpendicular to the figure

• A line that a figure is flipped over

• A line that divides a figure into two equal parts

What is the sum of the angles in a triangle?

• 360 degrees

• 90 degrees

• 180 degrees

• 270 degrees

How can you form a triangle from three angles that add up to 180 degrees?

• By drawing parallel lines

• By using exterior angles

• By using alternate interior angles

• By using vertical angles

What is an alternate interior angle?

• An angle that is on the same side of a transversal

• An angle that is opposite to another angle

• An angle that is adjacent to another angle

• An angle that is on opposite sides of a transversal