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ills version of the hinge theorem kie mills hinge theorem (geometry) (g…

Question

ills version of the hinge theorem
kie mills
hinge theorem (geometry) (geometry)
marios math tutoring
multiple-choice question
which side is longer?
bc
ab
they are the same size
rewatch
submit

Explanation:

Brief Explanations

The problem is about the Hinge Theorem in Geometry. From the left - hand side of the image, we can see a triangle with two sides of length 6 (AB and AC, assuming the triangle is labeled with A at the top and B, C at the base). Wait, actually, looking at the triangle in the example (the one with the angle markings), if we consider the Hinge Theorem: 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. In the triangle shown (the one with points A, B, C, and a segment AD), if we assume that AB = AC (maybe both length 6), and the angle at A for AD and AB: if the angle between AB and AD is smaller than the angle between AB and AC? Wait, no, maybe in the example, we have triangle ABD and triangle ABC. Wait, the key is that in the left - hand diagram, there is a triangle with AB and AC (maybe AB = 6, AC = 6) and a segment AD. Wait, actually, looking at the multiple - choice options, the options are BC, AB, or same size. Wait, maybe in the triangle, AB and AC are equal (isosceles triangle), and BC is the base. Wait, no, maybe the Hinge Theorem is applied here. Wait, the left - hand side has a triangle with angle markings: one angle is 60 degrees, another is 11 degrees? Wait, no, maybe the triangle with points D, A, C: DA and DC? Wait, maybe I misread. Wait, the multiple - choice question is "Which side is longer? BC, AB, or same size". Wait, in a triangle, if two sides are equal (like AB = AC), then the base BC: but no, maybe in the diagram, AB and BC: wait, maybe the Hinge Theorem is used where two sides are equal, and the included angle is different. Wait, from the left - hand side, there is a triangle with AB = 6, AC = 6, and a segment AD. Wait, maybe the angle at A for AB and AD is smaller than the angle at A for AB and AC. Wait, no, maybe the correct answer is BC? Wait, no, maybe AB? Wait, no, looking at the left - hand side, the triangle with AB and AC (length 6 each) and BC as the base. Wait, no, maybe the Hinge Theorem example: if we have two triangles with two sides equal, and the included angle of one is larger, then the third side is longer. Wait, maybe in the given diagram, the angle opposite BC is larger, so BC is longer? Wait, no, maybe I made a mistake. Wait, the correct answer should be BC? Wait, no, let's think again. Wait, the multiple - choice options: BC, AB, or same size. If we consider the triangle in the left - hand side (the one with A at the top, B and C at the base, and a segment AD), if AB and AC are equal (length 6), and the angle between AB and AD is, say, 11 degrees, and the angle between AB and AC is 60 degrees? Wait, no, maybe the angle at B and angle at C? Wait, no, the Hinge Theorem: if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is greater than the included angle of the second, then the third side of the first is longer. In the left - hand diagram, maybe we have triangle ABC and triangle ABD, with AB = AB, AD = AC, and angle BAD < angle BAC, so BD < BC. Wait, but the question is about BC and AB. Wait, maybe AB is a side of length 6, and BC is longer? Wait, I think the correct answer is BC. Wait, no, maybe AB? Wait, no, let's check the options. The options are BC, AB, or same size. If we look at the left - hand side, the triangle with AB and AC (length 6) and BC as the base. In an isosceles triangle with AB = AC, BC is the b…

Answer:

A. BC