Question

Triangle DEF is congruent to GHJ by the SSS theorem. Which rigid transformation is required to map DEF onto GHJ?

dilation
reflection
rotation
translation

Answer 1

Answer: The correct option is 4, i.e., translation.

Explanation:

It is given that the triangle DEF is congruent to GHJ by the SSS theorem.

From the given figure it is noticed that the triangle DEF and GHI are isosceles triangle.

Reason for correct option:

In transition the side and angles of the shape are not effected and the figure transfers from one place to another place without making any other change.

Since the both triangle are congruent and the position of all sides and angles are same, therefore option 4 is correct.

Reason for incorrect option:

In dilation the size of the figure is either stretched or compressed according to the scale factor k. But in the given figure the size of both triangles are same it means option A is incorrect.

In reflection the distance of all the point in preimage and all the image are same from the central line. Any central line does not exist in given figure. SO, the option B is incorrect.

In rotation the side length and angles are not affected but the position are not same, therefore the option C is incorrect.

Answer 2

Answer: Translation

Step-by-step explanation:

Given: Triangle DEF is congruent to GHJ by the SSS theorem.

From the given picture two sides of both triangles are equal therefore, the triangle DEF and GHI are isosceles triangle.

We know that a transition is a kind of rigid motion used in geometry to trace a function that moves an object a particular distance that maps produces images.

Since the both triangle are congruent and just position of triangle GHJ is shifted to the right and down.

Therefore, the  transition is rigid transformation which is required to map DEF onto GHJ