problem 10 thm 3 t 4310 Assume that D is between B and C as

problem 10

thm 3

t 4.3.10. Assume that D is between B and C, as shown in Figure 4.31. By Theorem In his today ca ge Unfortunately, his A ABC and AABD have angle sums less than 180 Which triangle, if any, has larger sum? Prove your answer. the work of Sac with 4.3.3 Giovanni The Italian priest How atics. Figure 4.3 l Triangles. published just aft Mund the time th *4.3.11, Generalize Corollary 4.3.4 to convex polygons with n sides. Prove your generalization

Solution

In given convex triangle,

let D be the mid point of BC

then area depends upon side AB & AC

as AD remains the common side

But here

D is more stretched towards C

Hence increasing BD

and AB > AC

Hence area of triangle ABD > triangle ACD