Question

determine whether the triangles are congruent. note the triangles are not drawn to scale. determine whether the triangles are congruent. note the triangles are not drawn to scale.

Explanation:

Step1: Find third - angle of first triangle

The sum of angles in a triangle is $180^{\circ}$. For the first triangle with angles $44^{\circ}$ and $35^{\circ}$, the third - angle $\theta_1=180-(44 + 35)=101^{\circ}$.

Step2: Find third - angle of second triangle

For the second triangle with angles $53^{\circ}$ and $44^{\circ}$, the third - angle $\theta_2=180-(53 + 44)=83^{\circ}$.

Step3: Check congruence conditions

The side - angle combinations of the two triangles do not match any of the congruence postulates (SAS, ASA, SSS, AAS, HL). The angles and sides are not in the same corresponding positions for congruence.

Answer:

Not congruent