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Q4) State the correspondence between the vertices, sides and angles of the following pairs of congruent triangles.

      (i) ABC   ​ XYZ                             (ii) ​ ABC   ​ YZX

      (iii) ​ PQR   ​ EFG                           (iv) ​ PRQ  EFG

Q5) Prove that the bisector of the top angle of an isosceles triangle bisects the base at right angles.

Q6) Show that in an isosceles triangle, the angles opposite equal sides are equal.(Hint. Draw a perpendicular to the unequal side from the vertex.)

Q7) In the isosceles ​ ABC , AB = AC. Perpendiculars BD and CE are drawn from the vertices B and C, to the opposite sides. Show that BD = CE.

Q8) In the square ABCD, show that the two triangles ABC and ADC are congruent to each other.


Dear student,

Question 5)

Given: In ABC, AD bisects BACBAD=CAD, & AB=AC  To Prove: ADB=90° and BD=CDProof:  In ADB & ADC AB=AC     --(given)BAD=CAD--( given) AD= AD -- (common)ADB ADC   (by SAS property) ADB=ADC  -- (CPCT)      ...(1)also, BD=CD --(CPCT)      ...(2)But we know that ADB+ADC=180°  ---(lie on straight line)ADB+ADB=180°2ADB=180°ADB=180°2ADB=90°    ...(3)Thus from (2) and (3) we get,The bisector of the top angle of an isosceles triangle bisects the base at right angles. 
Question 7)


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