diff -r f349e03bb41f Lib/random.py
--- a/Lib/random.py	Tue Mar 05 01:37:02 2013 -0500
+++ b/Lib/random.py	Sun Apr 07 14:53:30 2013 +0300
@@ -342,6 +342,16 @@
         http://en.wikipedia.org/wiki/Triangular_distribution
 
         """
+        # Sanity check. According to the doc low must be less or equal to
+        # high. And mode should be somewhere between these bounds.
+        if low > high:
+            raise ValueError('high cannot be less then low.')
+        if mode is not None and (mode < low or mode > high):
+            raise ValueError('mode must be between low and high.')
+
+        if high == low:
+            return low
+
         u = self.random()
         c = 0.5 if mode is None else (mode - low) / (high - low)
         if u > c:
diff -r f349e03bb41f Lib/test/test_random.py
--- a/Lib/test/test_random.py	Tue Mar 05 01:37:02 2013 -0500
+++ b/Lib/test/test_random.py	Sun Apr 07 14:53:30 2013 +0300
@@ -79,6 +79,28 @@
         shuffle(lst)
         self.assertTrue(lst != shuffled_lst)
 
+    def test_triangular(self):
+        """Check that triangular() correctly handles bad input. See issue 13355.
+        """
+        with self.assertRaises(ValueError):
+            # mode > high.
+            random.triangular(mode=2)
+            random.triangular(low=1, hihg=10, mode=11)
+            random.triangular(low=1, hihg=1, mode=11)
+
+            # mode < low.
+            random.triangular(mode=-1)
+            random.triangular(low=1, high=10, mode=0)
+            random.triangular(low=1, high=1, mode=0)
+
+            # low > high
+            random.triangular(low=5, high=2)
+            random.triangular(low=5, high=2, mode=1)
+            random.triangular(low=-2, high=-5)
+
+        self.assertEqual(random.triangular(low=10, high=10), 10)
+        self.assertEqual(random.triangular(low=10, high=10, mode=10), 10)
+
     def test_choice(self):
         choice = self.gen.choice
         with self.assertRaises(IndexError):
@@ -522,7 +544,7 @@
         for variate, args, expected in [
                 (g.uniform, (10.0, 10.0), 10.0),
                 (g.triangular, (10.0, 10.0), 10.0),
-                #(g.triangular, (10.0, 10.0, 10.0), 10.0),
+                (g.triangular, (10.0, 10.0, 10.0), 10.0),
                 (g.expovariate, (float('inf'),), 0.0),
                 (g.vonmisesvariate, (3.0, float('inf')), 3.0),
                 (g.gauss, (10.0, 0.0), 10.0),