Congruence and Proportionality Concepts

The video tutorial covers four main topics: proportional relationships using a tortoise and hare race, the relationship between weight and spring stretch using a spring scale, transformations to demonstrate scale copies of images, and the similarity of congruent figures with a scale factor of one. Each section provides detailed explanations and examples to help students understand these mathematical concepts.

In the race between the tortoise and the hare, if the tortoise runs 3 miles, how far does the hare run?

• 9 miles

• 12 miles

• 15 miles

• 18 miles

What does the slope of 4 represent in the context of the tortoise and hare race?

• The hare runs 4 times faster than the tortoise.

• The tortoise runs 4 times faster than the hare.

• The hare runs 4 miles for every mile the tortoise runs.

• The tortoise runs 4 miles for every mile the hare runs.

If a spring stretches 70 centimeters, how much weight in newtons is applied according to the proportional relationship?

• 98 newtons

• 140 newtons

• 77 newtons

• 50 newtons

What is the constant of proportionality in the spring scale example?

• 5/7

• 7/5

• 1/2

• 2/1

How do you determine if a smaller image is a scaled copy of a larger image?

• By using transformations like dilation and reflection.

• By using transformations like translation and rotation.

• By checking if they have the same area.

• By comparing their perimeters.

What transformation is used to match the smaller image to the larger one in the example?

• Translation

• Rotation

• Reflection

• Shear

What is true about congruent figures in terms of similarity?

• They are similar only if rotated.

• They are similar with a scale factor of 1.

• They are similar with a scale factor of 2.

• They are never similar.

If two figures are congruent, what can be said about their scale factor?

• It is greater than 1.

• It is equal to 1.

• It is less than 1.

• It varies depending on the figures.

Which statement is false about congruent figures?

• Congruent figures are always similar.

• Congruent figures are identical in shape and size.

• Congruent figures have a scale factor of 1.

• Congruent figures cannot be similar.

What happens to a figure when it is dilated with a scale factor of 1?

• It becomes larger.

• It changes shape.

• It becomes smaller.

• It remains the same size.