Triangle Properties and Proofs

The video tutorial covers the proof of a theorem stating that a triangle can have at most one obtuse angle. It explains the method of proof by contradiction, where assuming two angles are obtuse leads to a logical inconsistency. The tutorial also demonstrates proving triangle congruence using the Side-Side-Side (SSS) criterion and explores contradictions in angle assumptions, emphasizing the importance of logical reasoning in geometry.

What is the maximum number of obtuse angles a triangle can have?

• Three

• Two

• None

• One

What method does Eduardo use to prove the theorem about obtuse angles in a triangle?

• Inductive reasoning

• Empirical observation

• Proof by contradiction

• Direct proof

If two angles in a triangle are both greater than 90 degrees, what can be concluded?

• The triangle is isosceles

• The triangle is scalene

• The triangle is equilateral

• The triangle is not possible

Which theorem is used to reach a contradiction in Eduardo's proof?

• The isosceles triangle theorem

• The Pythagorean theorem

• The exterior angle theorem

• The sum of the angles in a triangle is 180 degrees

What does the SSS criterion stand for in triangle congruence?

• Angle-Angle-Side

• Side-Side-Side

• Side-Side-Angle

• Angle-Side-Angle

What property states that a segment is congruent to itself?

• Symmetric property

• Associative property

• Reflexive property

• Transitive property

What is the definition of congruent triangles?

• Triangles with equal perimeters

• Triangles that are identical in shape and size

• Triangles with equal side lengths

• Triangles with equal angles

If two angles in a triangle are equal, what can be said about the sides opposite these angles?

• They are unequal

• They are parallel

• They are perpendicular

• They are equal

What happens if an assumption in a geometric proof leads to a contradiction?

• The assumption is proven true

• The assumption is discarded

• The assumption is ignored

• The assumption is proven false

What conclusion can be drawn if assuming two angles are equal leads to a contradiction with given side lengths?

• The sides must be equal

• The sides cannot be equal

• The angles cannot be equal

• The angles must be equal