Subjects geometry

Sss Tabt Theorems 6Ae41D

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1. The problem involves solving a triangle using the SSS (Side-Side-Side) theorem and the TABT (The Angle Bisector Theorem). 2. The SSS theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. 3. The TABT states that the angle bisector divides the opposite side into segments proportional to the adjacent sides. 4. To solve, first use SSS to confirm triangle congruence or find missing angles using the Law of Cosines: $$c^2 = a^2 + b^2 - 2ab\cos(C)$$. 5. Then apply TABT: if angle bisector divides side $BC$ into $BD$ and $DC$, then $$\frac{AB}{AC} = \frac{BD}{DC}$$. 6. Use these relations to find unknown side lengths or angles step-by-step, substituting known values and simplifying. 7. Show intermediate steps with cancellation if simplifying fractions or ratios. 8. This approach fully solves the triangle using the given theorems.