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Understanding Shapes - II (Special Types of Quadrilaterals) — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsUnderstanding Shapes - II (Special Types of Quadrilaterals)5 Marks
Question
In the figure ABCD is a parallelogram, CE bisects $\angle\text{C}$ and AF bisects $\angle\text{A}$. In each of the following, if the statement is true, give a reason for the same.
  1. $\angle\text{A}=\angle\text{C}$
  2. $\angle\text{FAB}=\frac{1}{2}\angle\text{A}$
  3. $\angle\text{DCE}=\frac{1}{2}\angle\text{C}$
  4. $\angle\text{CEB}=\angle\text{FAB}$
  5. $\text{CE}\parallel\text{AF}$
✓

Answer


In parallelogram ABCD
CE is the bisector of $\angle\text{C}$ and and AF is the bisector of $\angle\text{A}$.
  1. $\angle\text{A}=\angle\text{C}$ (Opposite angles of a parallelogram)
  2. AF is the bisector of $\angle\text{A}$
$\angle\text{FAB}=\frac{1}{2}\angle\text{A}$
  1. CE is the bisector of $\angle\text{C}$
$\angle\text{DCE}=\frac{1}{2}\angle\text{C}$
  1. From (i), (ii) and (iii)
$\angle\text{FAB}=\angle\text{DCE}$
  1. $\angle\text{FAB}=\angle\text{DCE}$
But these are opposite angles of quadrilateral AECF
AB or AE || DC or FC
AECF is a parallelogram
CE || AF
Hence proved.

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