Question

lines, angles, and polygons
creating triangles from given side lengths: problem type 1
each figure below, the segments on the sides can be moved.
create the following triangles, if possible.
first figure: a triangle with side lengths of 3, 3, and 5.
second figure: a triangle with side lengths of 3, 5, and 9.
if there is no triangle possible with the given side lengths, click on
o triangle possible\.

Explanation:

To determine if a triangle can be formed with given side lengths, we use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

Step 1: Check the first figure (side lengths 3, 3, 5)

• Check the sum of the first two sides: \( 3 + 3 = 6 \). Since \( 6 > 5 \), this satisfies the triangle inequality.
• Check the sum of the first and third sides: \( 3 + 5 = 8 \). Since \( 8 > 3 \), this satisfies the triangle inequality.
• Check the sum of the second and third sides: \( 3 + 5 = 8 \). Since \( 8 > 3 \), this satisfies the triangle inequality.

Since all three conditions are met, a triangle can be formed with side lengths 3, 3, and 5.

Step 2: Check the second figure (side lengths 3, 5, 9)

• Check the sum of the first two sides: \( 3 + 5 = 8 \). Since \( 8 < 9 \), this does not satisfy the triangle inequality.

Since one of the conditions is not met, a triangle cannot be formed with side lengths 3, 5, and 9.

Answer:

• First figure: Triangle possible (side lengths 3, 3, 5)
• Second figure: No triangle possible (side lengths 3, 5, 9)