In triangle ABC, D and E are mid-points of
sides AB and BC respectively. Also, F is a
point in side AC so that DF is parallel to
BC.
(i) Prove that DBEF is a parallelogram.
(ii) Find the perimeter of parallelogram
DBEF, if AB = 10 cm, BC = 8.4 cm and
AC = 12 cm.
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Step-by-step explanation:
Given: D and E are mid points of AB and BC respectively. DF∥BC
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of AB
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF=
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF= 2
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF= 21
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF= 21
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF= 21 BC (I)
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF= 21 BC (I)Now, E and F are mid points of BC and AC respectively.Thus, by mid point theorem,
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF= 21 BC (I)Now, E and F are mid points of BC and AC respectively.Thus, by mid point theorem,EF∥AB or EF∥DB
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF= 21 BC (I)Now, E and F are mid points of BC and AC respectively.Thus, by mid point theorem,EF∥AB or EF∥DBSince, opposite sides are parallel to each other. Hence, DBEF is a parallelogram
Given: D and E are mid points of AB and BC respectively. DF∥BCSince, DF∥BC D is mid point of ABBy converse of mid point theorem, F is mid point of AC and DF= 21 BC (I)Now, E and F are mid points of BC and AC respectively.Thus, by mid point theorem,EF∥AB or EF∥DBSince, opposite sides are parallel to each other. Hence, DBEF is a parallelogramPerimeter of parallelogram = 2(BE+BD) (Opposite sides of parallelogram are equal)
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