We want to find the value of x, then describe the transformations that map △ EFG onto △ LMN. Let's begin by finding the value of x.
Finding the value of x
Note that the corresponding sides of the congruent triangles are congruent.
△ EFG ≅ △ LMN
⇓
Congruent Sides [0.5em]
EF≅LM
FG≅MN
EG≅LN
Segment MN is congruent to segment FG. This means that we can find the length of FG and equate it to the length of MN to find x. Notice that △ EFG is a right triangle. This means that we can use the Pythagorean Theorem to find the missing length of the hypotenuse FG. In this triangle, the lengths of the legs are 5 centimeters and 12 centimeters.
We found that the length of FG is 13 centimeters. Let's use this information to find the value of x.
NM&=x+3
& ⇒ x+3=13
FG&=13
We will solve this equation for x.
The value of x is 10. Now we will describe the transformations that map △ EFG onto △ LMN.
Identifying the Transformations
The orientation of the triangle is different, so we can first rotate △ EFG 180^(∘) clockwise about vertex G.
Next we need to translate the image of the rotation up to overlap with △ LMN.
One series of transformations that maps △ EFG onto △ LMN is a 180^(∘) clockwise rotation followed by an upward translation. Please note that this is just one example of a series of transformations and that there are many other possibilities.
