Hi, this problem is from the Prepswift video Similar Triangle Problems II. In the above, I was trying to use similarity statements to figure this out. If triangle ARB ~ triangle ARC, that means the side AR should be the same corresponding side for both triangles. So in calculating the area of both, AR could be either the height or base, but either way its the same for both. In the explanation video, Greg states that AR is the height for triangle ARC, but the base for triangle ARB. Why would this be the case? Why wouldn’t they both be the height, and therefore if they have the same height then the ratio of sides between the two triangles should be 1 to 1? Thanks!
You decide if it is the height or the base depending on the corresponding angles.
Hint: See where the angles ‘d’, and ‘x’ lie with reference to the side AR.
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Hmm interesting, so does this mean the similarity statements we could make about the two triangles are secondary in importance to the placement of the corresponding angle(s)? Meaning, RB and RC are not necessarily corresponding even though they have the same placements in the names of the triangles? Hopefully my clarify question makes sense lol.
I didn’t quite understand what you’re saying.
But basically, since all the angles are equal in both the triangles, both of them are similar.
Now, you need to place the 2 triangles side-by-side such that the corresponding angles match.
If you rotate the left triangle clockwise by 90 degrees, and place it next to the right triangle, you will notice that for both the triangles, the top angle is now ‘d’, the bottom angle for both is 90, and the right-side angle for both the triangles is ‘x’.
Now, you can say that the ratio of these corresponding sides is equal.
Meaning, BR/AR = BA/AC = AR/RC
I hope this helps.
Yes that makes sense. If they didn’t give us the x angle, how would we change our approach? Would it no longer be solvable? Thanks!
Yes.
You won’t be able to prove the similarity of triangles then.