Triangle abc is transformed to create triangle mnl. which statement is true? the transformation is rigid because corresponding side lengths and angles are congruent. the transformation is rigid because corresponding side lengths are congruent and corresponding angles are not congruent. the transformation is nonrigid because the two triangles have different names. the transformation is nonrigid because the three sides and the three angles in each triangle have different measures.

in this question, it is given that

triangle abc is transformed to create triangle mnl.

first we have to understand what are rigid transformations .

a rigid transformation is a transformation of the plane that preserves length. reflections, translations, rotations, and combinations of these three transformations are "rigid transformations".

and in rigid transformation, pre image and image are congruent .

and for the given question, all the sides and angles of triangle abc are congruent to triangle mnl.

so the correct option is the first option .

the correct answer is a

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4