Isosceles and Equilateral Triangles Explained

This video tutorial covers the final section of chapter four, focusing on isosceles and equilateral triangles. It begins with an overview of objectives, including finding missing angles and sides, and classifying triangles by side lengths. The video explains the properties of isosceles triangles, including legs, base, and angles, and explores the isosceles triangle theorem and its converse. Through examples, students learn to solve problems using these theorems. The tutorial also covers equilateral triangles, explaining their properties and related theorems. Advanced problems and challenges are presented to reinforce learning.

What are the two congruent sides of an isosceles triangle called?

• Base Angles

• Vertex

• Legs

• Base

In an isosceles triangle, what is the angle included by the legs called?

• Supplementary Angle

• Right Angle

• Vertex Angle

• Base Angle

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

• They are supplementary

• They are right angles

• They are congruent

• They are complementary

What is the converse of the isosceles triangle theorem?

• If two angles of a triangle are congruent, then the sides opposite those angles are congruent

• If two sides of a triangle are congruent, then the base angles are supplementary

• If one angle of a triangle is right, then the triangle is isosceles

• If the base angles are congruent, then the triangle is equilateral

If an isosceles triangle has two angles measuring 63 degrees, what is the measure of the third angle?

• 54 degrees

• 72 degrees

• 45 degrees

• 63 degrees

In an equilateral triangle, what is the measure of each angle?

• 90 degrees

• 45 degrees

• 60 degrees

• 120 degrees

What is the equilateral triangle theorem?

• If a triangle is equilateral, then it is also isosceles

• If a triangle is equilateral, then it is equiangular

• If a triangle is equilateral, then it has one right angle

• If a triangle is equilateral, then it is scalene

If a triangle is equiangular, what can be said about its sides?

• One side is longer than the other two

• They are all different lengths

• Two sides are equal

• All three sides are equal

In an equilateral triangle, if one side measures 14 units, what is the perimeter of the triangle?

• 28 units

• 42 units

• 56 units

• 21 units

In a challenge problem, if you have two equations with variables x and y, which method can you use to solve them?

• Factoring

• Graphing

• Substitution or Elimination

• Trial and Error