Exploring Isosceles and Equilateral Triangles

This video tutorial covers the properties and theorems of isosceles and equilateral triangles. It explains the key characteristics of these triangles, including congruent sides and angles, and provides several examples to illustrate how to solve problems involving these geometric shapes. The video also discusses the relationship between the angles and sides in these triangles and how to apply theorems to find unknown values.

What is the definition of an isosceles triangle?

• A triangle with no congruent sides

• A triangle with at least two sides congruent

• A triangle with all sides congruent

• A triangle with all angles equal

In an isosceles triangle, what are the angles opposite the congruent sides called?

• Right angles

• Base angles

• Vertex angles

• Supplementary angles

If two sides of a triangle are congruent, what can be said about the angles opposite those sides?

• They are right angles

• They are congruent

• They are supplementary

• They are complementary

Given an isosceles triangle with base angles of 70 degrees, what is the measure of the vertex angle?

• 140 degrees

• 110 degrees

• 70 degrees

• 40 degrees

In an isosceles triangle, if the base angles are 50 degrees each, what is the measure of the vertex angle?

• 50 degrees

• 60 degrees

• 80 degrees

• 100 degrees

What is the measure of each angle in an equilateral triangle?

• 90 degrees

• 60 degrees

• 120 degrees

• 45 degrees

If an equilateral triangle has a side length of 6x, what is the value of x if each side is 60 units?

• 10

• 5

• 20

• 15

In an isosceles triangle, if the vertex angle is 4x and each base angle is 2x + 10, what is the value of x?

• 25

• 20

• 15

• 10

If an isosceles triangle has a base of x and legs of 4x - 2, what is the value of x if the perimeter is 113?

• 11

• 12

• 14

• 13

In a triangle with angles x + 15, 3x - 35, and 4x, what is the value of x?

• 20

• 25

• 35

• 30