Geometry Concepts: Similarity and Transformations

The video tutorial covers Unit 2 topics, focusing on dilation, similarity, and slope. It includes exercises on determining the truth of statements about dilations, exploring triangle similarity, calculating slopes, and identifying similar polygons. The tutorial concludes with a practical dilation exercise using a specific scale factor.

What happens to the length of a line segment when it is dilated with a scale factor of 1?

• It becomes twice as long.

• It disappears.

• It becomes half as long.

• It remains the same length.

If two triangles have two pairs of congruent angles, what can be said about the third pair of angles?

• They are equal to 90 degrees.

• They are supplementary.

• They are complementary.

• They are also congruent.

Which of the following is true about the angles of a triangle when it is dilated?

• The angles become right angles.

• The angles remain unchanged.

• The angles double in measure.

• The angles become half their original measure.

How do you calculate the slope of a line using a slope triangle?

• Divide the vertical distance by the horizontal distance.

• Multiply the vertical distance by the horizontal distance.

• Divide the horizontal distance by the vertical distance.

• Subtract the horizontal distance from the vertical distance.

What is the slope of a line if the vertical distance is 4 and the horizontal distance is 5?

• 5/4

• 4/5

• 1/5

• 5/1

Which transformation involves changing the size of a figure but not its shape?

• Reflection

• Dilation

• Rotation

• Translation

What must be true for two polygons to be considered similar?

• They must have the same area.

• They must have congruent corresponding angles and proportional side lengths.

• They must be the same size.

• They must have the same perimeter.

If a triangle has sides of length 3, 4, and 5, and a similar triangle has a side of length 6, what is the length of the corresponding side in the similar triangle?

• 12

• 10

• 9

• 8

How do you find the length of a missing side in similar triangles?

• By adding the lengths of the known sides.

• By using the Pythagorean theorem.

• By setting up a proportion with the corresponding sides.

• By measuring the angles.

What is the equation of a line with a slope of 4/5 passing through the point (1, 3)?

• y = 5/4x - 1

• y + 3 = 4/5(x + 1)

• y = 4/5x + 3

• y - 3 = 4/5(x - 1)