Question

XYZ is a dilation of triangle ABC by a scale factor of 5. Which of the following proportions verified that triangle ABC and XYZ are similar?

Answer 1

Answer with explanation:

When ΔABC is dilated by a Scale factor of 5 we will get ΔX Y Z.

Pre-Image = ΔABC

Image = ΔX Y Z

When a triangle is dilated , then the two Triangles that is Original ΔABC and Triangle after dilation ΔX Y Z will be Similar.

⇒Similar triangles has Corresponding sides proportional as well as Corresponding Angles are congruent.

≡Corresponding congruent Angles are

→∠A=∠X

→∠B=∠Y

→∠C=∠Z

≡Corresponding congruent Sides are

`(AB)/(XY)=(AC)/(XZ)=(BC)/(YZ)`

The Proportionality statement which proves two triangles are Similar

Option B

`(AB)/(XY)=(AC)/(XZ)`

Answer 2

C. AB/XY = AC/XZ

Explanation:

Dilation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The original figure either stretches or shrinks by a certain factor.

In the problem, the dilation is by a factor of 5 and we can see that ABC shrinks to form XYZ.

So, ABC and XYZ are similar triangles which means that the ratio of their corresponding sides will be equal:

AB/XY = AC/XZ = BC/YZ = 5