State if the triangles in each pair are similar. if so, state how you know that they are similar and complete the similarity statement.

Triangle KLM ~ Triangle KQR

Similar, AA similarity

This is first choice.

Step-by-step explanation:

Even though the triangle isn't drawn to scale, we are suppose to assume those arrow things mean that that those pair of line segments are parallel.

The transversals of those parallel lines are RM and LQ.

Alternate interior angles are congruent.  This means the following pairs of angles are congruent:

Angle Q and L.

Angle R and M.

Since we have two pairs of angles from each triangle are congruent, then the two triangles are at least similar.

So we want to make a similarity statement:

Triangle KLM ~ Triangle KQR

The order matters.  I used what I knew about what angles were congruent.

So K was first on left side and K was first on the right side because they are congruent because they are vertical angles.

L was second on left side so Q was second on right side because they were congruent.

M was third on left side so R was third on right side because they were congruent.

77

step-by-step explanation:

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