+91-8076753736 support@wiredfaculty.com
logo
logo

Sponsor Area

Triangles

Question
CBSEENMA10007382
Wired Faculty App

Triangle ABC is right-angled at B and D is the mid-point of BC. Prove that AC2 = 4AD2 - 3AB2.

Solution
In right ∆ABC, by Pythagoras Theorem.
AC2 = BC2 + AB2...(i)
Similarly, in rt. ∆ABD,
AD2 = BD2 + AB2
                 space equals open parentheses 1 half BC close parentheses squared plus AB squared space space space space space space space space space space space space space space space space left square bracket because space BD space equals space 1 half BC right square bracket
                  <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>
rightwards double arrow                            4 AD squared space equals space BC squared plus 4 AB squared
rightwards double arrow                             BC squared space equals space 4 AD squared minus 4 AB squared         ...(ii)
From (i) and (ii), we  get
                         AC squared equals 4 AD squared minus 4 AB squared plus AB squared
space Hence comma space space space AC squared equals 4 AD squared minus 3 AB squared space space space space Proved

Some More Questions From Triangles Chapter

All _________ triangles are similar,(isosceles, equilateral)

Two polygons of the same number of sides are similar, if (a) their corresponding angles are ________ and (b) their corresponding sides are _________(equal, proportional).

Give two different examples of pair of 
(i) similar figures.
(ii) non-similar figures.

State whether the following quadrilaterals are similar or not:

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation