Question

Moment for Discovery SSS Theorem Via Kites and Darts Two geometric figures, the kite and dart, though elementary, are quite useful. The figures we have in mind are shown in Figure 3.26, where it is assumed that AB = AD and BC = CD. The dart is distinguished from the kite by virtue of the eight angles at A, B, C, and D involving the diagonals AC and BD being either all acute angles (for the kite), or two of them, such as the angles at C, being obtuse or right angles (for the dart). Because AC = AC, the two triangles on either side of line AC are congruent by SSS. However, this fact will follow from results preced- ing the SSS Theorem, thereby providing a way to prove the SSS criterion from kites and darts. Write out a proof, with the following steps to guide you. Figure 3.26

Answer 1

Given- I AABC S AXYZ So, By CPCT AB = ХУ BC=YZ AC=XZ As it is given that AB= AD BC =CD AD = ХУ CO = EZ AC=XZ AAOC ŠAXYZ by SSS theorem L 2 - According to given condition which says A is equidistant from B and D, G is eauidistant from B ando. It can be said that Acis perpendicular bisector of BD i BE = ED AC will Angle Bisector theorem states that bisect LBAD and LB C D In A ABE and A ADE A B = AD LABE = LADE AEAE So, BY SAS ДАВЕ 2 Дере

ZBAC = LDAC given and AXYZ Now it is In A ABC A B - XY BC=Yz AC = XZ So, BY SSS A ABC N property D X Y Z