What statement is needed to prove that ΔABC is similar to ΔDBA?
Segment BC is a hypotenuse.
Angle B is congruent to itself.
Segment BA is shorter than segment BC.
Segment BC is intersected by segment AD.
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whats hypotenuse ?
hypotenuse is the longest side of a right triangle.
telling us BC is a hypotenuse is not new info because they tell us angle CAB (marked with the little box) is a right angle, which makes BC a hypotenuse
if (but the did not) tell us AB was a hypotenuse, we could use that ...
so is the answer B ?
no. I think there is a problem with this question. None of the choices allow us to prove the triangles are similar.
in order to solve it you dont need any of those statements AT ALL ?
we do need to know that angle ADB = 90º
we would know that if they told us
1) angle ADB is a right angle, or
2) side AB is a hypotenuse, or
3) AD is perpendicular to BC
but they did not... so there is a problem with this question. Ask your teacher about it.
to make it more clear. the big triangle ABC has a right angle in it (we know because they mark angle BAC with a little square)
if we draw the little triangle like this