In , points , and are the mid–points of sides , and respectively. The lengths of the…

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadrilaterals · Quadrilaterals

Problem

\triangle ABC

, points

D

E

and

F

are the mid–points of sides

AB

AC

and

BC

respectively. The lengths of the sides of the triangle are

AB=14\text{ cm}

AC=10\text{ cm}

and

BC=18\text{ cm}

. (i) Find the lengths

AD

and

AE

. (ii) Using the information that

D

E

and

F

are mid-points, state the pairs of parallel line segments among

AD

AE

DF

and

FE

. (iii) Identify the nature of the quadrilateral

ADFE

and give one reason for your answer. (iv) Determine the perimeter of quadrilateral

ADFE