Mahabir Singh Solutions for Chapter: Triangles, Exercise 2: ACHIEVERS SECTION (HOTS)

Fill in the blanks.
(i) In the right triangles $\mathrm{\Delta }ABC$ and $\mathrm{\Delta }DEF$, if hypotenuse $AB=EF$ and side $AC=DE$, then $\mathrm{\Delta }ABC\cong$ P
(ii) If $\mathrm{\Delta }ABC$ is obtuse angled at a point B, then the longest side is Q
(iii) Difference of any two sides of a triangle is R than the third side.
         P            Q     R
(A) $\mathrm{\Delta }EFD$ $BC$ Greater
(B) $\mathrm{\Delta }EFD$ $AC$ Less
(C) $\mathrm{\Delta }DEF$ $AB$ Less
(D) $\mathrm{\Delta }DEF$ $AC$ Greater

Match the following.
Column I                                     Column II
P.                                              1. SAS Rule

$\mathrm{\Delta }AMB\cong \mathrm{\Delta }AMC$
Q.                                              2. RHS Rule

$\mathrm{\Delta }AOB\cong \mathrm{\Delta }POQ$
R.                                             3. SSS Rule

$\mathrm{\Delta }AOP\cong \mathrm{\Delta }BOQ$
S.                                             4. AAS Rule

$\mathrm{\Delta }AMB\cong \mathrm{\Delta }AMC$    

$ABC$ is a right triangle such that $AB=AC$ and bisector of angle $C$ intersects the side $AB$ at $D$. then $AC+AD=$ _______________