In the given figure, D is the mid-point of BC and E is any point on AD. Prove that :
(i) ar (△EBD) = ar (△EDC)
(ii) ar (△ABE) = ar (△ACE)

Question

In the given figure, D is the mid-point of BC and E is the mid-point of AD. Prove that : ar (ΔABE) = ar (ΔABC).

KnowledgeBoat · Accepted Answer

Median AD divides triangle ABC into two triangles ABD and ACD of equal area. ar (△ABD) = ar (△ABC) .....(1) Since E is the mid-point of AD, BE is the median of ΔABD. ar (△ABE) = ar (△ABD) .....(2) Substituting value from equation 1 in equation 2, we get : ar (△ABE) = ar (△ABE) = ar (△ABC). Hence, proved that ar (△ABE) = ar (△ABC).

Mathematics

In the given figure, D is the mid-point of BC and E is the mid-point of AD. Prove that : ar (ΔABE) = ar (ΔABC).

Theorems on Area

Related Questions

In the given figure, D is the mid-point of BC and E is any point on AD. Prove that :
(i) ar (△EBD) = ar (△EDC)
(ii) ar (△ABE) = ar (△ACE)

In the given figure, a point D is taken on side BC of ΔABC and AD is produced to E, making DE = AD. Show that :
ar (ΔBEC) = ar (ΔABC).

Mathematics

In the given figure, D is the mid-point of BC and E is the mid-point of AD. Prove that : ar (ΔABE) = ar (ΔABC).

Theorems on Area

Related Questions

In the given figure, D is the mid-point of BC and E is any point on AD. Prove that :(i) ar (△EBD) = ar (△EDC)(ii) ar (△ABE) = ar (△ACE)

In the given figure, a point D is taken on side BC of ΔABC and AD is produced to E, making DE = AD. Show that :ar (ΔBEC) = ar (ΔABC).

In the given figure, D is the mid-point of BC and E is any point on AD. Prove that :
(i) ar (△EBD) = ar (△EDC)
(ii) ar (△ABE) = ar (△ACE)

In the given figure, a point D is taken on side BC of ΔABC and AD is produced to E, making DE = AD. Show that :
ar (ΔBEC) = ar (ΔABC).