Properties of Isosceles and Equilateral Triangles

This lesson covers the definitions and properties of isosceles and equilateral triangles. It explains the isosceles triangle theorem, the properties of equilateral triangles, and their corollaries. The lesson also discusses converse theorems and the role of perpendicular bisectors in isosceles triangles.

What is the defining property of an isosceles triangle?

• It has a right angle

• All angles are equal

• Two sides are of the same length

• All sides are of different lengths

How many sides of equal length does an equilateral triangle have?

• One

• None

• Two

• Three

In an isosceles triangle, what are the sides of equal length called?

• Altitudes

• Hypotenuse

• Legs

• Base

What is the angle called that is formed by the two legs of an isosceles triangle?

• Vertex angle

• Base angle

• Right angle

• Supplementary angle

If a triangle is equilateral, what can be said about its angles?

• All angles are 45 degrees

• All angles are 90 degrees

• All angles are 60 degrees

• All angles are different

What is true about a triangle if it is equiangular?

• It must be scalene

• It must be equilateral

• It must be isosceles

• It must be right-angled

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

• They are different

• They are perpendicular

• They are parallel

• They are congruent

How can you identify an isosceles triangle?

• By having one right angle

• By having all angles equal

• By having all sides of different lengths

• By having two congruent sides

What happens if a line bisects the vertex angle of an isosceles triangle?

• It becomes an equilateral triangle

• It bisects the base perpendicularly

• It becomes a right triangle

• It bisects the base at an angle

If a line is the perpendicular bisector of the base of an isosceles triangle, what does it do to the vertex angle?

• It does not affect the vertex angle

• It makes the vertex angle 60 degrees

• It makes the vertex angle 90 degrees

• It bisects the vertex angle