diff --git a/geo-types/src/geometry.rs b/geo-types/src/geometry.rs
index 85b28bea4..4f4ac4abf 100644
--- a/geo-types/src/geometry.rs
+++ b/geo-types/src/geometry.rs
@@ -1,6 +1,6 @@
 use crate::{
     CoordinateType, GeometryCollection, Line, LineString, MultiLineString, MultiPoint,
-    MultiPolygon, Point, Polygon,
+    MultiPolygon, Point, Polygon, Rect, Triangle,
 };
 use num_traits::Float;
 use std::convert::TryFrom;
@@ -36,6 +36,8 @@ where
     MultiLineString(MultiLineString<T>),
     MultiPolygon(MultiPolygon<T>),
     GeometryCollection(GeometryCollection<T>),
+    Rect(Rect<T>),
+    Triangle(Triangle<T>),
 }
 
 impl<T: CoordinateType> From<Point<T>> for Geometry<T> {
@@ -74,6 +76,18 @@ impl<T: CoordinateType> From<MultiPolygon<T>> for Geometry<T> {
     }
 }
 
+impl<T: CoordinateType> From<Rect<T>> for Geometry<T> {
+    fn from(x: Rect<T>) -> Geometry<T> {
+        Geometry::Rect(x)
+    }
+}
+
+impl<T: CoordinateType> From<Triangle<T>> for Geometry<T> {
+    fn from(x: Triangle<T>) -> Geometry<T> {
+        Geometry::Triangle(x)
+    }
+}
+
 impl<T: CoordinateType> Geometry<T> {
     /// If this Geometry is a Point, then return that, else None.
     ///
diff --git a/geo-types/src/triangle.rs b/geo-types/src/triangle.rs
index 3cd4f137f..e2efaa9e5 100644
--- a/geo-types/src/triangle.rs
+++ b/geo-types/src/triangle.rs
@@ -1,7 +1,7 @@
 use crate::{polygon, Coordinate, CoordinateType, Line, Polygon};
 
 /// A bounded 2D area whose three vertices are defined by `Coordinate`s.
-#[derive(Copy, Clone, Debug, Hash)]
+#[derive(Copy, Clone, Debug, Hash, PartialEq)]
 #[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
 pub struct Triangle<T: CoordinateType>(pub Coordinate<T>, pub Coordinate<T>, pub Coordinate<T>);
 
diff --git a/geo/src/algorithm/map_coords.rs b/geo/src/algorithm/map_coords.rs
index d05b0c260..87b4e1929 100644
--- a/geo/src/algorithm/map_coords.rs
+++ b/geo/src/algorithm/map_coords.rs
@@ -36,7 +36,7 @@
 
 use crate::{
     Coordinate, CoordinateType, Geometry, GeometryCollection, Line, LineString, MultiLineString,
-    MultiPoint, MultiPolygon, Point, Polygon, Rect,
+    MultiPoint, MultiPolygon, Point, Polygon, Rect, Triangle
 };
 use std::error::Error;
 
@@ -416,6 +416,8 @@ impl<T: CoordinateType, NT: CoordinateType> MapCoords<T, NT> for Geometry<T> {
             Geometry::MultiLineString(ref x) => Geometry::MultiLineString(x.map_coords(func)),
             Geometry::MultiPolygon(ref x) => Geometry::MultiPolygon(x.map_coords(func)),
             Geometry::GeometryCollection(ref x) => Geometry::GeometryCollection(x.map_coords(func)),
+            Geometry::Rect(ref x) => Geometry::Rect(x.map_coords(func)),
+            Geometry::Triangle(ref x) => Geometry::Triangle(x.map_coords(func)),
         }
     }
 }
@@ -440,6 +442,8 @@ impl<T: CoordinateType, NT: CoordinateType> TryMapCoords<T, NT> for Geometry<T>
             Geometry::GeometryCollection(ref x) => {
                 Ok(Geometry::GeometryCollection(x.try_map_coords(func)?))
             }
+            Geometry::Rect(ref x) => Ok(Geometry::Rect(x.try_map_coords(func)?)),
+            Geometry::Triangle(ref x) => Ok(Geometry::Triangle(x.try_map_coords(func)?)),
         }
     }
 }
@@ -455,6 +459,8 @@ impl<T: CoordinateType> MapCoordsInplace<T> for Geometry<T> {
             Geometry::MultiLineString(ref mut x) => x.map_coords_inplace(func),
             Geometry::MultiPolygon(ref mut x) => x.map_coords_inplace(func),
             Geometry::GeometryCollection(ref mut x) => x.map_coords_inplace(func),
+            Geometry::Rect(ref mut x) => x.map_coords_inplace(func),
+            Geometry::Triangle(ref mut x) => x.map_coords_inplace(func),
         }
     }
 }
@@ -545,6 +551,57 @@ impl<T: CoordinateType> MapCoordsInplace<T> for Rect<T> {
     }
 }
 
+impl<T: CoordinateType, NT: CoordinateType> MapCoords<T, NT> for Triangle<T> {
+    type Output = Triangle<NT>;
+
+    fn map_coords(&self, func: impl Fn(&(T, T)) -> (NT, NT) + Copy) -> Self::Output {
+        let p1 = func(&self.0.x_y());
+        let p2 = func(&self.1.x_y());
+        let p3 = func(&self.2.x_y());
+
+        Triangle(
+            Coordinate { x: p1.0, y: p1.1 },
+            Coordinate { x: p2.0, y: p2.1 },
+            Coordinate { x: p3.0, y: p3.1 },
+        )
+    }
+}
+
+impl<T: CoordinateType, NT: CoordinateType> TryMapCoords<T, NT> for Triangle<T> {
+    type Output = Triangle<NT>;
+
+    fn try_map_coords(
+        &self,
+        func: impl Fn(&(T, T)) -> Result<(NT, NT), Box<dyn Error + Send + Sync>>,
+    ) -> Result<Self::Output, Box<dyn Error + Send + Sync>> {
+        let p1 = func(&self.0.x_y())?;
+        let p2 = func(&self.1.x_y())?;
+        let p3 = func(&self.2.x_y())?;
+
+        Ok(Triangle(
+            Coordinate { x: p1.0, y: p1.1 },
+            Coordinate { x: p2.0, y: p2.1 },
+            Coordinate { x: p3.0, y: p3.1 },
+        ))
+    }
+}
+
+impl<T: CoordinateType> MapCoordsInplace<T> for Triangle<T> {
+    fn map_coords_inplace(&mut self, func: impl Fn(&(T, T)) -> (T, T)) {
+        let p1 = func(&self.0.x_y());
+        let p2 = func(&self.1.x_y());
+        let p3 = func(&self.2.x_y());
+
+        let mut new_triangle = Triangle(
+            Coordinate { x: p1.0, y: p1.1 },
+            Coordinate { x: p2.0, y: p2.1 },
+            Coordinate { x: p3.0, y: p3.1 },
+        );
+
+        ::std::mem::swap(self, &mut new_triangle);
+    }
+}
+
 #[cfg(test)]
 mod test {
     use super::*;
diff --git a/geo/src/algorithm/to_postgis.rs b/geo/src/algorithm/to_postgis.rs
index 9616f63a7..6e84f2e17 100644
--- a/geo/src/algorithm/to_postgis.rs
+++ b/geo/src/algorithm/to_postgis.rs
@@ -88,6 +88,12 @@ impl ToPostgis<ewkb::Geometry> for Geometry<f64> {
             Geometry::GeometryCollection(ref p) => {
                 ewkb::GeometryT::GeometryCollection(p.to_postgis_with_srid(srid))
             }
+            Geometry::Rect(ref p) => {
+                ewkb::GeometryT::Polygon(p.to_polygon().to_postgis_with_srid(srid))
+            }
+            Geometry::Triangle(ref p) => {
+                ewkb::GeometryT::Polygon(p.to_polygon().to_postgis_with_srid(srid))
+            }
         }
     }
 }