Question

(d) can these be the side lengths of a triangle?
5 cm, 3 cm, 7 cm
○ yes
triangles with these measurements
○ no
select
must be congruent.
are not necessarily congruent.

Explanation:

Step1: Check triangle inequality

The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side.

• $5 + 3 > 7$ → $8 > 7$ (True)
• $5 + 7 > 3$ → $12 > 3$ (True)
• $3 + 7 > 5$ → $10 > 5$ (True)

Step2: Analyze congruence

Triangles with identical side lengths are fixed in shape and size (SSS congruence rule), so all triangles with these side lengths must be congruent.

Answer:

Yes
must be congruent.