Triangle Similarity and Transformations

This video tutorial covers scaling and projections in geometry, focusing on scaling rectangles and polygons, understanding dilations and similarity, and exploring slope and line equations. It provides examples and exercises to help students grasp these concepts, emphasizing the importance of scale factors and angle measures. The tutorial also includes practical applications of equations for lines, enhancing problem-solving skills in geometry.

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

• 18 cm by 4.5 cm

• 13 cm by 4 cm

• 10 cm by 2 cm

• 6 cm by 1.5 cm

What is the scale factor if a rectangle with dimensions 12 by 8 is a scaled copy of a rectangle with dimensions 15 by 10?

• 4/5

• 5/4

• 3/2

• 2/3

If a point is 3 units away from the center of dilation and the scale factor is 2, how far will the image of the point be from the center?

• 12 units

• 9 units

• 3 units

• 6 units

When two polygons are similar, what remains unchanged?

• Perimeter

• Angle measures

• Side lengths

• Area

If triangle ABC is a dilation of triangle DEF with a scale factor of 2, what is the largest angle measure in triangle DEF if the largest angle in triangle ABC is 82 degrees?

• 41 degrees

• 82 degrees

• 164 degrees

• Cannot be determined

What transformation is used to complete the construction of a square from segment AC?

• Reflect segment AC over the x-axis

• Translate segment AC 5 units up

• Rotate segment AC 90 degrees counterclockwise using C as the center

• Rotate segment AC 90 degrees clockwise using C as the center

Why are two equilateral triangles always similar?

• They have the same area

• They have the same perimeter

• They have equal angle measures

• They have the same side lengths

How do you determine if two triangles are similar based on their side lengths?

• The triangles have the same area

• The triangles have equal side lengths

• The triangles have the same perimeter

• The triangles have proportional side lengths

What is the slope of a line that rises 2 units and runs 3 units?

• 1/3

• 2/3

• 3/2

• 1/2

If a line passes through the points (0, 5) and (2, 8), what is the slope of the line?

• 2/3

• 1/2

• 3/2

• 5/2