Question

Now, determine whether the relationship between the two triangles you found in the first task is true for any two triangles. For any line, if you draw two right triangles using the line as the hypotenuse, can the triangles be congruent? Why or why not? Do they have to be congruent? Why or why not?

Answer 1

Answer:

They are not congruent based on the drawing. I don't know what they mean by "do they have to be congruent?", as they don't have to be congruent unless the teacher is asking for them to be congruent.

Step-by-step explanation:

Congruency in geometry is defined as identical in form, meaning that it must follow CPCTC (and can be proven in many different ways).

In the case of the given triangles they are not congruent, as DE and AD do not share congruency with BA and CB, respectively. At best, the two given triangles are similar triangles, as ΔADE is a 2x scale factor of ΔCBA.

I am not sure what the question about "do they have to be congruent" is for. Obviously they aren't congruent and so they don't have to be? There is nothing that states they have to be congruent. If you are aiming for congruency, lines AB & CB's measurements would simply have to match that of ED & AD, respectively.

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Answer 2

Answer:

The relationship we found is that:

• The triangles have same vertical/horizontal segment ratio or slope.

But this doesn't indicate the triangles are congruent. They have different side lengths which makes them similar but not congruent.

They can be congruent if corresponding sides are of same length.