Question

question 2 (multiple choice worth 4 points)
(02.04r mc)

what conclusion can be made for c and e?
diagram with triangle and quadrilateral elements, angles at c: 36.5° and 27.8°, marked equal sides

options:

• c ≥ e
• c ≤ e
• c > e
• c < e

Explanation:

Step1: Identify congruent sides

We see $AC = AC$ (common side), $BC = DC$ (marked congruent).

Step2: Compare included angles

Angle for side $c$: $\angle ACB = 36.5^\circ$
Angle for side $e$: $\angle ACD = 27.8^\circ$
$36.5^\circ > 27.8^\circ$

Step3: Apply SAS inequality theorem

In two triangles, if two sides are congruent, the longer side is opposite the larger included angle. So $c > e$.

Answer:

c > e