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Describing Triangles

Describing Triangles 1.6 - Solution

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The base angles theorem tells us that two sides in a triangle are congruent, then the angles opposite them are congruent. But the opposite is true as well. If two angles are congruent then the sides opposite them are congruent. Looking at the given diagram, we see that AB.\angle A \cong \angle B. Thus, ACBC.\overline{AC} \cong \overline{BC}.

Remember that congruent sides have equal length. With this, we can set up an equation. AC=BC4x3=3x+8\begin{gathered} AC=BC\\ \Downarrow\\ 4x-3=3x+8 \end{gathered} Let's solve this equation.
4x3=3x+84x-3=3x+8
4x=3x+114x=3x+11
x=11x=11
We can now substitute x=11x=11 in the given expressions to obtain the side lengths of the triangle.
Side Expression of the Length Substitution Side Length
AC\overline{AC} 4x34x-3 4(11)34({\color{#0000FF}{11}})-3 AC=41AC=41
BC\overline{BC} 3x+83x+8 3(11)+83({\color{#0000FF}{11}})+8 BC=41BC=41