Question 1099847: 1. What additional information do you need to prove triangle GHI is congruent to triangle DEF?
Triangles GHI and DEF are shown. Side GH and DE are marked as congruent. Angles H and E are also marked as congruent.
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(1 point)
a) Line HI congruent to line EF
b) Line HI congruent to line ED
c) Angle F congruent to angle G
d) Line GI congruent to line DF
I'm struggling, could someone please help me?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The answers should talk about "side" or "segment" not "line,
because. Line goes on forever in both directions, with no end,
and we are talking about segments with two ends.
You have one angle and one side adjacent to that angle.
Your teacher expects you to memorize and apply "rules" taint in class,
but a kindergartener can figure this out if we change the word "congruent" to "superimposable."
If you can move, and/or rotate, and or flip one triangle
so that it exactly superimposed on the other,
those triangles are congruent.
In case your teacher insists,
finding that the other side of the congruentangle is congruent
(not DE=GH, but EF=HI) world give you
one pair of congruent angles flanked by pairs of congruent sides,
which your teacher calls side-angle-side (or SAS) congruence.
You know that sides DE and GH are congruent,
and so are the angles at H and E.
So you could superimpose vertices E and H,
and rotate and /or flip so that you get D and G superimposed
while keeping H and E superimposed.
That will place line segments EF and HI on the same ray
(the side of angle GHI=DEF that has I and F)
The question is whether F and I are at the same point on that line.
Maybe one of those points is closer to point H=E.
If EF and HI are congruent, F would also end up superimposed, and that proves the triangles are congruent, So a) is enough to prove congruent.
NOTES: You can name triangles by listing the letters for the vertices in any order,
but when teachers say that two triangles are congruent,
they call the triangles with 3-letter sequences that have the congruent angles and sides in the same position. They would say that DEF is congruent to GHI.
That makes the sides you knew were congruent from the start be the first two letters,
and the angles you knew were congruent from the start are the middle letter.
Once you superimpose congruent,sides and congruent angles, you cannot get F to superimpose with G, because vertex D from triangle DEF is already there,
so choice c) is ridiculous.
Something similar goes on with b) . ED and DE are the same side by a different name, and that side is congruent with GH, so we superimposed side GH from triangle GHI . We are not going to superimpose HI there too. Then G and I would be the same point, and GHI would not be a triangle.
Finally, the other option, option a) is tricky, because it would work sometimes, but it depends.
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