IfΔDEF~ΔABC and DE=AB, what is the relation between the two triangles?a)They are both right triangles.b)ΔDEF ≠ ΔABCc)They are both equilateral.d)ΔDEF ≅ ΔABCCorrect answer is option 'D'. Can you explain this answer?

Question

If&#916;DEF~&#916;ABC and DE=AB, what is the relation between the two triangles?&#8203;a)They are both right triangles.b)&#916;DEF &#8800; &#916;ABCc)They are both equilateral.d)&#916;DEF &#8773; &#916;ABCCorrect answer is option 'D'. Can you explain this answer?

Answer

Since DE=AB means that there ratio is 1 which means corresponding sides are equal.Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length.So they are congruent.

Answer

Since both the triangles are similar.....DE/AB=EF/BC so,DE.BC=AB.EF BC=EF...........(1) similarly DF=AC........(2) also DE=AB.......(3) ∆DEF congruent ∆ABC

Answer

They r congruent to each other

Answer

Given Information:

DEF~ABC (DEF is similar to ABC)
DE = AB

Explanation:

To understand the relation between the two triangles, let's analyze the given information and the properties of similar triangles.

1. Similar Triangles:

When two triangles are similar, it means that they have the same shape but may have different sizes. In similar triangles, the corresponding angles are equal, and the corresponding sides are proportional.

2. Corresponding Sides:

In the given question, it is mentioned that DE is equal to AB. This implies that DE and AB are corresponding sides of the two triangles. Therefore, we can conclude that the sides of DEF and ABC are proportional.

3. Proportional Sides:

If the sides of two triangles are proportional, it means that the ratio of the lengths of corresponding sides is the same. In this case, DE/AB = EF/BC = DF/AC.

4. Relation between the Triangles:

From the above information, we can conclude that the triangles DEF and ABC are similar because their corresponding sides are proportional. Hence, the correct answer is option 'D' - DEF ~ ABC.

Therefore, the relation between the two triangles is that they are similar (DEF ~ ABC).

Answer

DE/AB=EF/BC=DF/AC

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