Question

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 ALL OF THE QUESTIONS OR DONT ANSWER AT ALL THANK YOU.

Answer 1

Answer:

The triangles can be congruent but not always.

The triangles do not have to be congruent, but they have to be similar.

Step-by-step explanation:

See the attached diagram with this answer.

For any line (say OP), if you draw two right triangles ( Δ ABC and Δ A'B'C') using the line, OP as the hypotenuse, then the triangles can be congruent. This will be only when AC = A'C'.

That means if we draw two right triangles using the same length of a straight line as hypotenuse, then only the two right triangles will be congruent.

Now, If AC = A'C' then automatically, it becomes AB = A'B' and BC = B'C' and then by SSS criteria, the triangles Δ ABC and Δ A'B'C' will be congruent i.e. Δ ABC ≅ Δ A'B'C'.

But the triangles Δ ABC and Δ A'B'C' do not have to be congruent but they have to be similar.

Because, $\frac{A'B'}{AB} = \frac{B'C'}{BC} = \frac{A'C'}{AC}$

If this ratio becomes 1 : 1 then only those triangle will be congruent otherwise they will be similar only. (Answer)