Question

Which descriptions from the list below accurately describe the relationship between  ABC and  DEF? Check all that apply

5-3-7,10-6-14

A.
Congruent

B.
Same shape

C.
Similar

D.
Same size

Answer 1

Answer:

similar

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Step-by-step explanation:

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Answer 2

Given:

Two triangles ABC and DEF with measurement of their sides. AB= 5units, BC= 3units, AC= 7units, DE= 10units, EF= 6units, DF= 14units

To find:

The relationship between triangles ABC and DEF.

Solution:

To find the relationship between the given triangles, first, we find the ratio of corresponding sides.

So,

$\frac{AB}{DE} = \frac{5}{10} = \frac{1}{2}$

$\frac{BC}{EF} = \frac{3}{6} = \frac{1}{2}$

$\frac{AC}{DF} = \frac{7}{14} = \frac{1}{2}$

Hence,

$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$

As the ratio of corresponding sides of given triangles is the same so, the triangles are similar by SSS criterion.

If the triangles are similar, then they have the same shape but, not necessarily the same size.

The corresponding sides of the given triangles ABC and DEF are not equal. Hence, they are non-congruent and unequal in size but have the same shape.

So, the given triangles ABC and DEF have the same shape and they are similar.

The correct options are- B. same shape and C. similar.