Properties of Similar Triangles and Dilations

The video covers 8th-grade geometry topics, focusing on scaling, projections, and transformations. It explains how to determine if rectangles and polygons are scaled copies, using examples and calculations. The video also introduces dilations, transformations, and the concept of slope, providing methods to write equations for lines. Advanced topics include similarity in polygons and triangles, with practical applications of these concepts.

Which of the following pairs of dimensions could be a scaled copy of a rectangle measuring 12 cm by 3 cm?

• 6 cm by 1.5 cm

• 18 cm by 4.5 cm

• 10 cm by 2 cm

• 13 cm by 4 cm

If a rectangle with dimensions 12 cm by 8 cm is a scaled copy of another rectangle with dimensions 15 cm by 10 cm, what is the scale factor?

• 4/5

• 5/4

• 3/2

• 2/3

What is the effect of a dilation with a scale factor of 2 on the side lengths of a triangle?

• The side lengths are tripled.

• The side lengths are doubled.

• The side lengths remain the same.

• The side lengths are halved.

Which of the following statements is true about similar polygons?

• They have the same side lengths.

• They have different side lengths and angles.

• They have the same angle measures.

• They have different angle measures.

If two triangles are similar and one has a side length of 3 cm while the corresponding side of the other is 9 cm, what is the scale factor?

• 2

• 1/2

• 3

• 1/3

Which of the following statements is true about similar triangles?

• They have different angle measures.

• They are always congruent.

• They have the same angle measures.

• They always have the same side lengths.

If two triangles are similar and one has a side length of 4 while the corresponding side in the other triangle is 10, what is the scale factor?

• 3

• 1.5

• 0.4

• 2.5

What is the slope of a line that rises 2 units for every 3 units it runs horizontally?

• 3/2

• 1/3

• 1/2

• 2/3

Which equation represents a line with a slope of 2 and a y-intercept of -3?

• y = -2x + 3

• y = 2x - 3

• y = -2x - 3

• y = 2x + 3

If a triangle is dilated with a scale factor of 1/2, what happens to its side lengths?

• They double.

• They remain the same.

• They are halved.

• They triple.