Isosceles Triangle Theorem Concepts

The video tutorial covers the isosceles triangle theorem, its proof, and its converse. It begins by defining an isosceles triangle and stating the theorem, which asserts that if two sides of a triangle are congruent, the angles opposite those sides are also congruent. The video then outlines a strategy to prove the theorem using an angle bisector and congruent triangles. The proof is executed step-by-step, demonstrating the congruence of smaller triangles and concluding with the theorem's proof. Additionally, the video mentions a corollary about the bisector of the vertex angle and states the converse of the theorem, known as the base angles theorem.

What is the defining characteristic of an isosceles triangle?

• It has a right angle.

• All angles are equal.

• At least two sides are congruent.

• All sides are equal.

According to the isosceles triangle theorem, what can be said about the angles opposite the congruent sides?

• They are right angles.

• They are congruent.

• They are supplementary.

• They are complementary.

What is the main goal of the video tutorial?

• To prove the isosceles triangle theorem.

• To define different types of triangles.

• To measure angles in triangles.

• To solve complex triangle problems.

What is the first step in proving the isosceles triangle theorem?

• Identify the midpoint of the base.

• Construct a perpendicular bisector.

• Measure the angles.

• Construct an angle bisector.

What is the significance of the angle bisector in the proof of the isosceles triangle theorem?

• It helps in proving the congruence of two smaller triangles.

• It is used to find the area of the triangle.

• It measures the angles accurately.

• It divides the triangle into two equal parts.

Which postulate is used to prove the congruence of the two smaller triangles in the proof?

• Angle-Angle-Side

• Angle-Side-Angle

• Side-Side-Side

• Side-Angle-Side

What property is used to state that segment AD is congruent to itself?

• Transitive Property

• Symmetric Property

• Substitution Property

• Reflexive Property

What does the corollary to the isosceles triangle theorem state about the angle bisector?

• It is perpendicular to the base at its midpoint.

• It is parallel to the base.

• It bisects the base.

• It forms an obtuse angle with the base.

What is the converse of the isosceles triangle theorem also known as?

• Perpendicular Bisector Theorem

• Midpoint Theorem

• Base Angles Theorem

• Vertex Angle Theorem

According to the converse of the isosceles triangle theorem, if two angles are congruent, what can be said about the opposite sides?

• They are parallel.

• They are congruent.

• They are perpendicular.

• They are equal in length.