Question

version of the hinge theorem
ills
e theorem (geometry) (geometry)
os math tutoring
multiple-choice question
which angle is larger?
∠atc
they are the same size.
∠sat
rewatch

Explanation:

To determine which angle is larger, we use the Hinge Theorem (also known as the SAS Inequality 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 third side of the first triangle is longer than the third side of the second triangle. Conversely, if two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is longer than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.

Looking at the triangles involved (implied by the context of the Hinge Theorem in the image), we can assume that the sides adjacent to ∠SAT and ∠ATC are congruent (or follow the Hinge Theorem setup). If the third side opposite ∠SAT is longer than the third side opposite ∠ATC, then ∠SAT is larger than ∠ATC. From the visual and the Hinge Theorem application, ∠SAT is the larger angle.

Answer:

C. ∠SAT