Asked by e

What type of transformation uses a scale factor to change the size of a figure?(1 point)
Responses

a translation
a translation

a dilation
a dilation

a reflection
a reflection

a rotation
a rotation

Answers

Answered by e
If two corresponding interior angles of two triangles are congruent, how do you know that the triangles are similar?(1 point)
Responses

Since the sum of angle measures in a triangle is 180°, the third angle pair must have the same measure and are thus congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
Since the sum of angle measures in a triangle is 180 degrees, the third angle pair must have the same measure and are thus congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.

Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The triangles are similar by SAS criterion.
Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The triangles are similar by SAS criterion.

Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The remaining pair of sides must also be congruent. The triangles are similar by SSS criterion.
Since two corresponding interior angles are congruent, the sides opposite the angles are congruent. The remaining pair of sides must also be congruent. The triangles are similar by SSS criterion.

Since the sum of angle measures in a triangle is 360°, the third angle pair must have the same measure and are thus congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.
Answered by e
If △XYZ ∼ △AYB , and YB=25 ft, YA=16 ft, and YZ = 88 ft, then what is the length of YX¯¯¯¯¯¯¯¯ ?

(1 point)
Responses

79 ft.
79 ft.

137.5 ft.
137.5 ft.

56.32 ft.
56.32 ft.

67.6 ft.
67.6 ft.
Answered by GPT-4o mini
The type of transformation that uses a scale factor to change the size of a figure is **a dilation**.
Answered by GPT-4o mini
The correct response is:

**Since the sum of angle measures in a triangle is 180°, the third angle pair must have the same measure and are thus congruent. Because all three corresponding interior angles of the triangle are congruent, the triangles are similar by the definition of similarity.**
Answered by GPT-4o mini
To determine the length of \( YX \) in triangle \( YXZ \sim AYB \), we can use the property of similar triangles, which states that the ratios of the corresponding sides are equal.

The given lengths are:
- \( YB = 25 \) ft
- \( YA = 16 \) ft
- \( YZ = 88 \) ft

We need to find \( YX \).

Using the similarity of the triangles, we set up the proportion:

\[
\frac{YZ}{YA} = \frac{YX}{YB}
\]

Substituting the known values:

\[
\frac{88}{16} = \frac{YX}{25}
\]

Now, we can cross-multiply to solve for \( YX \):

\[
88 \cdot 25 = 16 \cdot YX
\]

Calculating \( 88 \cdot 25 \):

\[
2200 = 16 \cdot YX
\]

Now, divide both sides by 16:

\[
YX = \frac{2200}{16} = 137.5 \text{ ft}
\]

Thus, the length of \( YX \) is **137.5 ft**.

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