Understanding Isosceles Triangles and Congruency

The video tutorial explores the properties of isosceles triangles, focusing on proving that if two sides are congruent, the base angles are also congruent, and vice versa. It uses triangle congruency theorems like SSS and AAS to establish these properties. The tutorial also discusses the role of the midpoint and perpendicular bisectors in isosceles triangles, providing a comprehensive understanding of their geometric properties.

What defines an isosceles triangle?

• All sides are equal.

• Two sides are equal.

• All angles are equal.

• Two angles are equal.

What are the angles called that are between the congruent sides and the base in an isosceles triangle?

• Complementary angles

• Supplementary angles

• Base angles

• Vertex angles

Which congruency theorem is used to prove that two triangles are congruent when all three sides are equal?

• ASA (Angle-Side-Angle)

• SAS (Side-Angle-Side)

• AAS (Angle-Angle-Side)

• SSS (Side-Side-Side)

If the base angles of an isosceles triangle are congruent, what can be inferred about the sides?

• The sides are perpendicular.

• The sides are parallel.

• The sides are congruent.

• The sides are unequal.

What is the term for a line segment that is perpendicular to a side of a triangle and bisects it?

• Angle bisector

• Perpendicular bisector

• Median

• Altitude

Which congruency theorem is used when two angles and a non-included side are known?

• ASA (Angle-Side-Angle)

• SAS (Side-Angle-Side)

• SSS (Side-Side-Side)

• AAS (Angle-Angle-Side)

What is the result when two triangles are congruent?

• Their corresponding angles and sides are equal.

• Their areas are equal.

• Their altitudes are equal.

• Their perimeters are equal.

What is the significance of point D in the context of the isosceles triangle discussed?

• It is the center of the circle.

• It is the vertex of the triangle.

• It is the midpoint of the base.

• It is the endpoint of the altitude.

What is the relationship between the base angles and the legs in an isosceles triangle?

• If base angles are unequal, legs are equal.

• If base angles are equal, legs are equal.

• If base angles are equal, legs are unequal.

• If base angles are unequal, legs are unequal.

What additional property does the perpendicular bisector of the base of an isosceles triangle have?

• It is also the angle bisector.

• It is also the circumcenter.

• It is also the altitude.

• It is also the median.