Add compatibility check badges to READMEs. (#8288)

Author: ylil93

README.rst

@@ -1,7 +1,7 @@
 Core Library for Google Client Libraries
 ========================================
 
-|pypi| |versions|
+|pypi| |versions| |compat_check_pypi| |compat_check_github|
 
 This library is not meant to stand-alone. Instead it defines
 common helpers used by all Google API clients. For more information, see the
@@ -12,6 +12,10 @@ common helpers used by all Google API clients. For more information, see the
 .. |versions| image:: https://img.shields.io/pypi/pyversions/google-api_core.svg
  :target: https://pypi.org/project/google-api_core/
 .. _documentation: https://googleapis.github.io/google-cloud-python/latest/core/
+.. |compat_check_pypi| image:: https://python-compatibility-tools.appspot.com/one_badge_image?package=google-api-core
+ :target: https://python-compatibility-tools.appspot.com/one_badge_target?package=google-api-core
+.. |compat_check_github| image:: https://python-compatibility-tools.appspot.com/one_badge_image?package=git%2Bgit%3A//github.com/googleapis/google-cloud-python.git%23subdirectory%3Dapi_core
+ :target: https://python-compatibility-tools.appspot.com/one_badge_target?package=git%2Bgit%3A//github.com/googleapis/google-cloud-python.git%23subdirectory%3Dapi_core
 
 
 Supported Python Versions
@@ -20,4 +24,4 @@ Python >= 3.5
 
 Deprecated Python Versions
 --------------------------
-Python == 2.7. Python 2.7 support will be removed on January 1, 2020.
+Python == 2.7. Python 2.7 support will be removed on January 1, 2020.