切れる and 切る: snapping, cutting, and ability
Compare a snapped string with cutting, and use context to distinguish intransitive 切れる from the potential form of 切る.
A changed string and the use of scissors
靴ひもが切れました。 means that a shoelace snapped. Intransitive 切れる, read きれる, describes a break in something previously continuous.
はさみで糸を切りました。 says that someone cut thread with scissors. 切る, read きる, becomes 切りました in the polite past and 切って in the te-form.
The potential form is also 切れる
このはさみなら、厚い紙も切れます。 means that these scissors can cut even thick paper. Here 切れる is the potential form of 切る.
A report that paper came apart differs from a judgment about being able to cut it. 紙が切れた in isolation can be ambiguous; check the tool, situation, and surrounding speech.
A disconnected call and an expired pass
話の途中で電話が切れました。 says that a call was disconnected mid-conversation. 電話を切りました instead presents someone ending the call.
定期券の有効期限が切れています。 describes a commuter pass whose validity has expired. Nothing has been physically cut; the issue is whether the pass is currently valid.
What does 切れます mean in このはさみなら厚い紙も切れます?
Show the answer and why
It expresses ability: these scissors can cut even thick paper. Distinguish it from intransitive 切れました in 靴ひもが切れました, where a shoelace snapped.