Triangles ABD and CBD are shown. Triangle A B C is divided into two smaller triangles which are triangle A B D and D B C which share a common side B D. Point D lies on segment A C. Segment A D is congruent to segment C D. If m∠ADB = 110°, what is the relationship between AB and BC? AB < BC AB > BC AB = BC AB + BC < AC

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sharmajohn052 sharmajohn052 · Answer 1 · 2022-09-23T02:47:36+02:00

Step-by-step explanation:

ΔABC and ΔABD are two triangles on the same base AB.

To show :

ar(ABC)=ar(ABD)

Proof :

Since the line segment CD is bisected by AB at O. OC=OD.

In ΔACD, We have OC=OD.

So, AO is the median of ΔACD

Also we know that median divides a triangle into two triangles of equal areas.

∴ar(ΔAOC)=ar(ΔAOD) _______ (1)

Similarly , In ΔBCD,

BO is the median. (CD bisected by AB at O)

∴ar(ΔBOC)=ar(ΔBOD) _______ (2)

On adding equation (1) and (2) we get,

ar(ΔAOC)+ar(ΔBOC)=ar(ΔAOD)+ar(ΔBOD)

∴ar(ΔABC)=ar(ΔABD)