8/6 x 9/9 = 72/54
12/9 x 6/6 = 72/54
72/54 = 72/54
They are similar.
Triangle ABC is similar to triangle PQR
choice C is correct
The clockwise sequence of vertices MNO is the opposite of the counterclockwise sequence of vertices M'N'O', so it seems some sort of reflection is involved.
Length NO is 3 times length N'O', but length NM is only 7/3 times length N'M', so the figures are not similar. (The ratios of side lengths must be the same for the figures to be similar.)
Choice D includes only rigid transformations that would ensure congruence. Similar figures may also differ by a dilation factor, so C is the better choice.
In short, only answer choice D is false. Everything else is true.
A. The ordering of FGH and LMN is important. This is because F and L pair up as the first letters of the triple letter sequences, so do G and M as the second letters. Segment FG pairs up with LM because we're talking about the first two letters of both sequences. At the same time, FH and LN pair up because they are composed of the first and third letters of FGH and LMN respectively. Due to the triangles being similar, we can say FG/LM = FH/LN, ie we have a proportion.
B. Segment LN is proportional to FH, as explained back in part A. For example, FH could be 10 times longer than LN, making FH = 10*LN. Once the scale factor is set, you must use it for the other pairs of sides as well.
C. Similar triangles have corresponding angles that are congruent. This means F = L, G = M and H = N. Dividing the measure of F over the measure of L leads to 1 (regardless of what the angles happen to be) due to the rule x/x = 1, where x is nonzero. The same thing happens with dividing the measures of angle G over angle M. We get 1 on both sides after simplifying this given equation, so it is a true equation.
D. Similar triangles are not congruent, so their corresponding side lengths are not congruent either.
E. As explained back in part C, the corresponding angles are congruent because we know the triangles to be similar. The ordering of the letters matter. Angles H and N are the third letters of FGH and LMN respectively, which is why they pair up and are congruent.
Check the picture below.
Check the picture below.
The sides and angles are congruent, because:
The sides are proportionate.
The angles are proportionate because they are touching each other.
The Side- Angle- Side Postulate would be correct when the triangle is equal to TRU.
I hope this helped!
Brainliest answer is always appreciated!