Question

Use the figure below to answer the question that follows:

Answer 1

What must be given to prove that \[\Delta \]BHG = \[\Delta \]CHI?

angle GBH = angle ICH and angle BGH = CIH (I think this one is it)
line BH = line CH and line BG = line CI
angle GBH = angle ICH and angle BHG = CHI
line BH = line CH and line HG = line HI

Answer 2

Sorry if this is confusing, I'm new to OpenStudy >_>

Answer 3

And might want to make another account without the heart symbol.. :\ Your account will not have a SmartScore...

Answer 4

Let's look at the choices:
A. angle GBH = angle ICH and angle BGH = CIH (I think this one is it)
This choice gives you two pairs of congruent angles.
Then you can use the pair of vertical angles (BHG & CHI), and you will have 3 pairs of congruent angles.
With just 2 pairs of congruent angles, you cna prove the triangles are similar but not congruent.
Choice A is not the answer.

Answer 5

B. line BH = line CH and line BG = line CI
Using these two pairs of congruent sides plus the pair of vertical angles, you get SSA.
There is no SSA method of proving triangles congruent, so choice B is not it.

Answer 6

C. angle GBH = angle ICH and angle BHG = CHI
Here you are given again two pairs of congruent angles. One of the pairs you could figure out yourself since the angles are vertical. This can let you prove the triangles are similar but not congruent. Choice C is not the answer either.

Answer 7

By the process of elimination, choice D must be the answer, but let's look at it anyway.

Answer 8

D. line BH = line CH and line HG = line HI
Here you are given two pairs of congruent sides.
In between the two sides of each triangle, there is an included angle.
The included angles are congruent because they are vertical angles.
That means you have SAS. SAS is a valid way of proving triangles congruent.
That means choice D is the correct answer.

Answer 9

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