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Triangles — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsTriangles4 Marks
Question
Read the Source/ Text given below and answer these questions:

Hareesh and Deep were trying to prove a theorem. For this they did the following:
$i.$ Drew a $\triangle ABC.$
$ii. D$ and $E$ are found as the mid points of $AB$ and $AC.$
$iii. DE$ was joined and $DE$ was extended to $F$ so $DE = EF.$
$iv. FC$ was joined.
Answer the following questions:
$i. \triangle\text{ADE}$ and $\triangle\text{EFC}$ are congruent by which criteria$?$
$\text{SSS}$
$\text{RHS}$
$\text{SAS}$
$\text{ASA}$
$ii. \angle\text{EFC}$ is equal to which angle$?$
$a. \angle\text{DAE}$
$b. \angle\text{ADE}$
$c. \angle\text{AED}$
$d.  \angle\text{B}$
$iii. \angle\text{ECF}$ is equal to which angle$?$
$a. \angle\text{DAE}$
$b. \angle\text{ADE}$
$c. \angle\text{AED}$
$d.  \angle\text{B}$
$iv. CF$ is equal to which of the following$?$
$a. BD$
$b. CE$
$c. AE$
$d.  EF$
$v. CF$ is parallel to which of the following$?$
$a. AE$
$b. CE$
$c. BD$
$d.  EF$
✓

Answer

$(i)$ $(c)$ $\text{SAS}$
$(ii)$ $(b)$ $\angle\text{ADE}$
$(iii)$ $(a)$ $\angle\text{DAE}$
$(iv)$ $(a)$ $BD$
$(v)$ $(c)$ $BD$

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