diff --git a/crates/fj-kernel/src/algorithms/triangulate/delaunay.rs b/crates/fj-kernel/src/algorithms/triangulate/delaunay.rs
index 7449f7735..c54aa508d 100644
--- a/crates/fj-kernel/src/algorithms/triangulate/delaunay.rs
+++ b/crates/fj-kernel/src/algorithms/triangulate/delaunay.rs
@@ -18,6 +18,7 @@ pub fn triangulate(points: Vec<Local<Point<2>>>) -> Vec<[Local<Point<2>>; 3]> {
             *v1.local_form(),
             *v2.local_form(),
         ])
+        .expect("invalid triangle")
         .winding_direction();
 
         let triangle = match orientation {
diff --git a/crates/fj-math/src/line.rs b/crates/fj-math/src/line.rs
index f69ff0374..4c07cac56 100644
--- a/crates/fj-math/src/line.rs
+++ b/crates/fj-math/src/line.rs
@@ -1,4 +1,4 @@
-use crate::{Point, Vector};
+use crate::{Point, Triangle, Vector};
 
 /// An n-dimensional line, defined by an origin and a direction
 ///
@@ -33,6 +33,33 @@ impl<const D: usize> Line<D> {
         }
     }
 
+    /// Determine if this line is coincident with another line
+    ///
+    /// # Implementation Note
+    ///
+    /// This method only returns `true`, if the lines are precisely coincident.
+    /// This will probably not be enough going forward, but it'll do for now.
+    pub fn is_coincident_with(&self, other: &Self) -> bool {
+        let other_origin_is_not_on_self = {
+            let a = other.origin;
+            let b = self.origin;
+            let c = self.origin + self.direction;
+
+            // The triangle is valid only, if the three points are not on the
+            // same line.
+            Triangle::from_points([a, b, c]).is_some()
+        };
+
+        if other_origin_is_not_on_self {
+            return false;
+        }
+
+        let d1 = self.direction.normalize();
+        let d2 = other.direction.normalize();
+
+        d1 == d2 || d1 == -d2
+    }
+
     /// Create a new instance that is reversed
     #[must_use]
     pub fn reverse(mut self) -> Self {
@@ -102,6 +129,19 @@ mod tests {
 
     use super::Line;
 
+    #[test]
+    fn is_coincident_with() {
+        let line = Line::from_points([[0., 0.], [1., 0.]]);
+
+        let a = Line::from_points([[0., 0.], [1., 0.]]);
+        let b = Line::from_points([[0., 0.], [-1., 0.]]);
+        let c = Line::from_points([[0., 1.], [1., 1.]]);
+
+        assert!(line.is_coincident_with(&a));
+        assert!(line.is_coincident_with(&b));
+        assert!(!line.is_coincident_with(&c));
+    }
+
     #[test]
     fn convert_point_to_line_coords() {
         let line = Line {
diff --git a/crates/fj-math/src/triangle.rs b/crates/fj-math/src/triangle.rs
index 92dc8ec37..f4cd21888 100644
--- a/crates/fj-math/src/triangle.rs
+++ b/crates/fj-math/src/triangle.rs
@@ -21,7 +21,7 @@ impl<const D: usize> Triangle<D> {
     /// # Panics
     ///
     /// Panics, if the points don't form a triangle.
-    pub fn from_points(points: [impl Into<Point<D>>; 3]) -> Self {
+    pub fn from_points(points: [impl Into<Point<D>>; 3]) -> Option<Self> {
         let points = points.map(Into::into);
 
         let area = {
@@ -31,9 +31,9 @@ impl<const D: usize> Triangle<D> {
 
         // A triangle is not valid if it doesn't span any area
         if area != Scalar::from(0.0) {
-            Self { points }
+            Some(Self { points })
         } else {
-            panic!("Invalid Triangle specified");
+            None
         }
     }
 
@@ -103,7 +103,7 @@ where
     P: Into<Point<D>>,
 {
     fn from(points: [P; 3]) -> Self {
-        Self::from_points(points)
+        Self::from_points(points).expect("invalid triangle")
     }
 }