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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

1. BD is one of the diagonals of a quad ABCD .AM & CM are the perpendiculars from A & C,on BD. Show that ar(ABCD)=1/2BD(AM+CN).

2. ABCD is a trap. in which AB||CD.E is the midpoint of AD.If F is a point on BC such that segment EF is parallel to side DC, show that EF =1/2(AB+CD).

1]see ar abcd = ar abd + ar bcd ar abd=1/2*am*bd ar bcd=1/2*cn*bd ar abcd=1/2*am*bd+1/2cn*bd ar abcd=1/2 bd[am+cn]

2]extend ad and bc to intersect at o now a na b are mid points of od and oc resp . =>ab=1/2dc also ef //dc so f is mid point in tri ods ef = 3/4 dc ef=1/2[ab+dc]

1) Area of ΔABD = 1/2 × BD × AM Area of ΔBCD = 1/2 × BD × CN

ARea of quad ABCD = Area of ΔABD + Area of ΔBCD = = 1/2 × BD × AM + 1/2 × BD × CN = 1/2 × BD ( AM + CN)

2) Draw the diagonal BD such that it cuts EF at G

Consider ΔADB EG parallel AB (Since EF || AB) E is mid point of AD (given) By converse of Basic Proportionality Theorem (BPT) G is the mid point of BD (1)

By BPT EG = 1/2 (AB) ...........I Consider ΔBCD GF || CD (since AB || CD and EF || AB) G is midpoint of BD (from (1)) By converse of BPT F is midpoint of BC

By BPT, GF = 1/2 (CD) .......II

Now, In trap ABCD, EF = EG + GF = 1/2 (AB) + 1/2 (CD) = 1/2 (AB + CD)