IM Geometry Unit 3 CYR

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape the same, using a center point and a scale factor.

Front

What does it mean for two figures to be congruent?

Back

Two figures are congruent if they have the same size and shape.

Front

What is the scale factor in a dilation?

Back

The scale factor is the ratio of the length of a side of the image to the length of the corresponding side of the original figure.

Front

If a point A is dilated using a center C and a scale factor of k, what happens to the distance from C to A?

Back

The distance from C to A is multiplied by the scale factor k.

Front

What is the relationship between the lengths of corresponding sides of similar figures?

Back

The lengths of corresponding sides of similar figures are proportional.

Front

In triangle ABC, if angle A is 90 degrees and AB = 1 unit, AC = 8 units, how do you find BC?

Back

Use the Pythagorean theorem: BC = √(AB² + AC²) = √(1² + 8²) = √(1 + 64) = √65, which is about 8.1 units.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they are in the same plane and do not intersect, no matter how far they are extended.

Front

What is the difference between congruent and similar figures?

Back

Congruent figures are the same size and shape, while similar figures have the same shape but may differ in size.

Front

If a dilation has a scale factor of 2.5, how does it affect the lengths of the sides of a figure?

Back

Each side of the figure will be multiplied by 2.5, making the figure larger.