Question

question 8 (multiple choice worth 4 points) (02.04r mc) what conclusion can be made for c and e?

Explanation:

Step1: Analyze the triangles

We have two triangles $\triangle ABC$ and $\triangle ADC$. In $\triangle ABC$ and $\triangle ADC$, $AC = AC$ (common side), $BC = CD = 4$ (given).

Step2: Apply the Hinge Theorem

The Hinge Theorem states that if two sides of one triangle are congruent to two sides of another triangle, but the included angle of the first triangle is larger than the included angle of the second triangle, then the side opposite the larger included angle is longer.
Here, in $\triangle ABC$ and $\triangle ADC$, $\angle BCA=36.5^{\circ}$ and $\angle DCA = 27.8^{\circ}$, and $36.5^{\circ}>27.8^{\circ}$.
Since in $\triangle ABC$, side $AB = c$ is opposite $\angle BCA$ and in $\triangle ADC$, side $AD=e$ is opposite $\angle DCA$.

Answer:

$c > e$