Question

Unit #2: Scale Drawings, Simila

Question
Select all the true statements.
a. Dilations always increase the length of line segments.
b. Dilations take perpendicular lines to perpendicular lines.
C. Dilations of an angle are congruent to the original angle.
d. Dilations increase the measure of angles.
e. Dilations of a triangle are congruent to the original triangle.
f. Dilations of a triangle are similar to the original triangle.

Answer 1

True statements about dilations are that they take perpendicular lines to perpendicular lines, dilations of an angle are congruent to the original angle, and dilations of a triangle are similar to the original triangle. Dilations do not always increase the length of line segments, do not increase the measure of angles, and do not produce triangles that are congruent unless the scale factor is one.

Step-by-step explanation:

Selecting all the true statements about dilations from the provided options:

• b. Dilations take perpendicular lines to perpendicular lines. This is true since dilations in geometry preserve the angles between lines, thus if two lines are perpendicular before the dilation, they will remain perpendicular afterwards.
• c. Dilations of an angle are congruent to the original angle. This is true as the size of the angles remains unchanged in a dilation.
• f. Dilations of a triangle are similar to the original triangle. True, because dilations produce a figure which maintains the shape but alters the size, keeping the corresponding angles the same and the lengths of sides proportional.

Here are the false statements that were listed:

• a. Dilations always increase the length of line segments. This is false; dilations can also decrease lengths if the scale factor is less than one.
• d. Dilations increase the measure of angles. This is false as dilations do not alter angles.
• e. Dilations of a triangle are congruent to the original triangle. This is false since dilations change the size of the triangle, though they remain similar; they are not congruent unless the scale factor is one.

Answer 2

In the context of Mathematics, particularly geometry, dilations preserve the shape of figures and angles, so perpendicular lines remain perpendicular and angles remain congruent after the transformation. Dilations also result in similar but not congruent figures, as they change the size while preserving the shape. The scale can increase or decrease segment lengths.

The subject of this question is Mathematics, specifically dealing with scale drawings and similar figures in geometry. Here are the true statements:

• b. Dilations take perpendicular lines to perpendicular lines. This is true because a dilation is a transformation that produces an image that is the same shape as the original, just a different size. If two lines are perpendicular before the dilation, they will remain perpendicular after the dilation.
• c. Dilations of an angle are congruent to the original angle. True, because dilations do not change angle measures.
• f. The dilations of a triangle are similar to the original triangle. This is also true since dilations produce figures that have the same shape but are a different size than the original.

Other options can be explained as follows:

• a. Dilations always increase the length of line segments. This is false as dilations can either increase or decrease the length depending on whether the scale factor is greater than or less than 1.
• d. Dilations increase the measure of angles. This is false because dilation does not change the measure of angles.
• e. The dilations of a triangle are congruent to the original triangle. This is false as congruent figures must be the same size and shape, while dilated figures are only guaranteed to be the same shape.