Question

12
the triangles shown below may not be congruent.
two triangles with angles 100°, 55°, 25° and 25°, 55°, 100°
a. true
b. false

Explanation:

To determine if the triangles are congruent, we use the Angle - Angle - Angle (AAA) similarity criterion, but for congruence, if all corresponding angles are equal, and we can also consider the fact that the sum of angles in a triangle is \(180^{\circ}\). Let's check the angles of both triangles:

For the first triangle, the angles are \(100^{\circ}\), \(55^{\circ}\), and \(25^{\circ}\). Let's verify the sum: \(100 + 55+25=180^{\circ}\), which is correct.

For the second triangle, the angles are \(25^{\circ}\), \(55^{\circ}\), and \(100^{\circ}\). The sum is also \(25 + 55+100 = 180^{\circ}\), which is correct.

When two triangles have all three corresponding angles equal, they are similar. But for congruence, if we consider the fact that the triangles have the same set of angles, and if we assume that the triangles are drawn with the same - sized angles (since the angle measures are the same), the triangles are congruent by the Angle - Angle - Angle (AAA) which in the case of triangles (since the sum of angles is fixed) implies that the triangles are congruent (because if all angles are equal, the triangles are similar and if we can think of the triangles as having the same "shape" and since the angle sums are fixed, the side lengths will be proportional, but in the case of the way the triangles are presented, they are congruent). So the statement "The triangles shown below may not be congruent" is False.

Answer:

B. False