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Which descriptions from the list below accurately describe the relationship between ΔABC and ΔDEF?
CHECK ALL THAT APPLY.

A. Same Area
B. Same Size
C. Congruent
D. Congruent after a dilation

CORRECT ANSWER GETS BRAINLIEST Which descriptions from the list below accurately describe the relationship between ΔABC and ΔDEF CHECK ALL THAT APPLY A Same Are class=

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leandro272047

D i think dilations are my favorite in math

The relationship between ΔABC and ΔDEF is that they are congruent after a dilation. So, option D is correct. The dilation occurs with a scale factor of 2.

What does congruent mean in geometry?

  • Two geometric figures are said to be congruent or to be in the relation of congruence if it is possible to superpose one of them on the other so that they coincide throughout.
  • The word congruent or congruency means exactly equal in shape and size, irrespective of flipping or rotating a shape.

What is dilation and how it is calculated?

  • Dilation is the process of resizing or transforming an object.
  • It is a transformation that makes the objects smaller or larger with the help of the given scale factor.
  • The new figure obtained after dilation is called the image and the original image is called the pre-image.
  • Dilation can be of two types: i) Expansion and ii) Contraction.
  • A scale factor is a number by which the size of any geometrical figure or shape can be changed concerning its original size.
  • Scale factor = Dimension of the new shape ÷ Dimension of the original shape.

Finding the relationship between the given triangles:

Given two triangles as ΔABC and ΔDEF.

ΔABC has dimensions as AC = 3, BC = 4 and AB = 5

∠A = 53°, ∠B=37°, and ∠C=90°

ΔDEF has dimensions as DF = 6, EF = 8 and DE = 10

∠D = 53°, ∠E = 37° and ∠F = 90°

From the dimensions, both the triangles have similar measures of angles but different sizes.

Since the sizes are different, the triangles are not congruent.

Area of the triangle = [tex]\frac{1}{2}[/tex] × B × h

For  ΔABC, B= AC=3 and h=BC=4

Area =  [tex]\frac{1}{2}[/tex] × B × h

        =  [tex]\frac{1}{2}[/tex] × 3 × 4

        = 6

For ΔDEF, B=DF=6, h=EF=8

Area =  [tex]\frac{1}{2}[/tex] × B × h

        =  [tex]\frac{1}{2}[/tex] × 6 × 8

        = 24

Thus, the areas of the two triangles are different.

Checking for the dilation:

Since the triangles have the same angle and the same shape, the dilation may take place. Thus, finding the scale factor for the ΔDEF (New image) and ΔABC (pre-image).

Scale factor = Dimension of the new shape ÷ Dimension of the original shape

The dimensions for ΔABC are (AC, CB, BA) = (3, 4, 5)

The dimensions for ΔDEF are (DF, FE ,ED) = (6, 8, 10)

On dividing the dimensions,

Scale factor = 2 i.e., (6/3, 8/4, 10/5)

This means the ΔDEF undergoes dilation with a scale factor of 2.

So, the new image ΔDEF has original dimensions as (3, 4, 5) i.e., similar to the ΔABC.

Therefore, after dilation, the ΔABC and ΔDEF are congruent (as they have the same size and same angles).

So, option D is correct.

Learn more about the dilation and congruency here:

https://brainly.com/question/10253650

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