D, E, F are respectively the mid-points of sides AB, BC and CA a
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    Triangles

    Multiple Choice QuestionsLong Answer Type

    201.

    In the given fig, D is a point on the side BC of ∆ABC such that ∠ADC = ∠BAC. Prove that <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>  or  CA2 = CB.CD.


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    202. Sides AB and AC and median AD of triangle ABC are respectively proportional to sides PQ and PR and median PM of another triangle PQR. Show that ∆ABC ~ ∆PQR.
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    203. A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
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    204. If AD and PM are medians of triangles ABC and PQR, respectively where ∆ABC ~ ∆PQR, prove that <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>
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    Multiple Choice QuestionsShort Answer Type

    205. Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.
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    206.

    Diagonals of a trapezium ABCD with AB || DC intersect each other at the point O.If AB = 2 CD, find the ratio of the areas of triangles AOB and COD.

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    Multiple Choice QuestionsLong Answer Type

    207.

    In the given fig, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show thatspace space fraction numerator ar left parenthesis increment ABC right parenthesis over denominator ar left parenthesis increment DBC right parenthesis end fraction equals AO over DO.

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    208. If the areas of two similar triangles are equal, then the triangles are congruent i.e., equal and similar triangles are congruent.
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    209. D, E, F are respectively the mid-points of sides AB, BC and CA and of ∆ABC. Find the ratio of the areas of ∆DEF and ∆ABC.

    Given: ∆ABC in which D, E and F are the mid points of the sides BC,

    Given: ∆ABC in which D, E and F are the mid points of the sides BC, CA and AB respectively.
    Find fraction numerator ar left parenthesis increment DEF right parenthesis over denominator ar left parenthesis increment ABC right parenthesis end fraction equals ?
    ∵    F and E are the mid points sides AB and AC respectively.
              rightwards double arrow space space space space space space space space space space space space space space space space space space space space space space space FE parallel to BC
    and                            FE equals 1 half BC
                                                    [Mid-point theorem]
            rightwards double arrow          FE parallel to BD
    and                 FE equals BD
              rightwards double arrow     BDEF is a parallelogram.
    Similarly, we can prove DCEF is a parallelogram. Now, in ∆DEF and ∆ABC
    ∠DEF = ∠B [opposite angles of parallelogram]
    and    ∠DFE = ∠C
    Therefore, by using AA similar condition
    increment DEF tilde increment ABC
    rightwards double arrow space space space space space space space fraction numerator ar left parenthesis increment DEF right parenthesis over denominator ar left parenthesis increment ABC right parenthesis end fraction equals DE squared over AB squared equals open parentheses begin display style 1 half end style AB close parentheses squared over AB squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator begin display style 1 fourth end style AB squared over denominator AB squared end fraction equals 1 fourth

    Hence,    fraction numerator ar left parenthesis increment DEF right parenthesis over denominator ar left parenthesis increment ABC right parenthesis end fraction equals 1 fourth.
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    210. Prove that the ratio of the areas of two similar triangle is equal to the square of the ratio of their corresponding medians.
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