diff --git a/lib/matplotlib/bezier.py b/lib/matplotlib/bezier.py
index 714a57933bb5..0877038d5776 100644
--- a/lib/matplotlib/bezier.py
+++ b/lib/matplotlib/bezier.py
@@ -31,8 +31,9 @@ def get_intersection(cx1, cy1, cos_t1, sin_t1,
     c, d = sin_t2, -cos_t2
 
     ad_bc = a * d - b * c
-    if ad_bc == 0.:
-        raise ValueError("Given lines do not intersect")
+    if np.abs(ad_bc) < 1.0e-12:
+        raise ValueError("Given lines do not intersect. Please verify that "
+                         "the angles are not equal or differ by 180 degrees.")
 
     # rhs_inverse
     a_, b_ = d, -b
diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
index a6120d645008..2d7d609dc50d 100644
--- a/lib/matplotlib/patches.py
+++ b/lib/matplotlib/patches.py
@@ -2789,8 +2789,8 @@ class Angle3(_Base):
         """
         Creates a simple quadratic Bezier curve between two
         points. The middle control points is placed at the
-        intersecting point of two lines which crosses the start (or
-        end) point and has a angle of angleA (or angleB).
+        intersecting point of two lines which cross the start and
+        end point, and have a slope of angleA and angleB, respectively.
         """
 
         def __init__(self, angleA=90, angleB=0):
@@ -2827,9 +2827,9 @@ class Angle(_Base):
         """
         Creates a piecewise continuous quadratic Bezier path between
         two points. The path has a one passing-through point placed at
-        the intersecting point of two lines which crosses the start
-        (or end) point and has a angle of angleA (or angleB).  The
-        connecting edges are rounded with *rad*.
+        the intersecting point of two lines which cross the start
+        and end point, and have a slope of angleA and angleB, respectively.
+        The connecting edges are rounded with *rad*.
         """
 
         def __init__(self, angleA=90, angleB=0, rad=0.):
diff --git a/lib/matplotlib/tests/baseline_images/test_arrow_patches/connection_styles.png b/lib/matplotlib/tests/baseline_images/test_arrow_patches/connection_styles.png
new file mode 100644
index 000000000000..8255d0d3bf58
Binary files /dev/null and b/lib/matplotlib/tests/baseline_images/test_arrow_patches/connection_styles.png differ
diff --git a/lib/matplotlib/tests/test_arrow_patches.py b/lib/matplotlib/tests/test_arrow_patches.py
index a6416954ca33..b1ef1e298ef7 100644
--- a/lib/matplotlib/tests/test_arrow_patches.py
+++ b/lib/matplotlib/tests/test_arrow_patches.py
@@ -1,3 +1,4 @@
+import pytest
 import matplotlib.pyplot as plt
 from matplotlib.testing.decorators import image_comparison
 import matplotlib.patches as mpatches
@@ -133,3 +134,34 @@ def test_arrow_styles():
                                          arrowstyle=stylename,
                                          mutation_scale=25)
         ax.add_patch(patch)
+
+
+@image_comparison(baseline_images=['connection_styles'], extensions=['png'],
+                  style='mpl20', remove_text=True)
+def test_connection_styles():
+    styles = mpatches.ConnectionStyle.get_styles()
+
+    n = len(styles)
+    fig, ax = plt.subplots(figsize=(6, 10))
+    ax.set_xlim(0, 1)
+    ax.set_ylim(-1, n)
+
+    for i, stylename in enumerate(sorted(styles)):
+        patch = mpatches.FancyArrowPatch((0.1, i), (0.8, i + 0.5),
+                                         arrowstyle="->",
+                                         connectionstyle=stylename,
+                                         mutation_scale=25)
+        ax.add_patch(patch)
+
+
+def test_invalid_intersection():
+    conn_style_1 = mpatches.ConnectionStyle.Angle3(angleA=20, angleB=200)
+    p1 = mpatches.FancyArrowPatch((.2, .2), (.5, .5),
+                                  connectionstyle=conn_style_1)
+    with pytest.raises(ValueError):
+        plt.gca().add_patch(p1)
+
+    conn_style_2 = mpatches.ConnectionStyle.Angle3(angleA=20, angleB=199.9)
+    p2 = mpatches.FancyArrowPatch((.2, .2), (.5, .5),
+                                  connectionstyle=conn_style_2)
+    plt.gca().add_patch(p2)