Triangles Unit Test

Question

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Question
A triangle has sides a
, b
, and c
. Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed if a=3
, b=4
, and c=5
.

Option A: Yes, a right triangle can be formed.

Option B: No, a right triangle cannot be formed.

Choose 1 for Option A or 2 for Option B.

(1 point)

Answer 1

To determine whether a triangle with sides \( a = 3 \), \( b = 4 \), and \( c = 5 \) can be a right triangle using the Converse of the Pythagorean Theorem, we can check if \( a^2 + b^2 = c^2 \).

Calculating the squares:

• \( a^2 = 3^2 = 9 \)
• \( b^2 = 4^2 = 16 \)
• \( c^2 = 5^2 = 25 \)

Now, checking the equation:

\[ a^2 + b^2 = 9 + 16 = 25 \] \[ c^2 = 25 \]

Since \( a^2 + b^2 = c^2 \), this confirms that a right triangle can be formed.

So, the answer is:

Option A: Yes, a right triangle can be formed.

Choose 1 for Option A.