Solving Equations and Triangle Properties

This video tutorial explains how to use the properties of isosceles triangles to find unknown values. It covers the congruence of sides and angles, and demonstrates solving for variables x and y using these properties. The tutorial includes two examples, highlighting the use of the isosceles triangle theorem and the triangle sum theorem to determine angle measures and side lengths.

What defines an isosceles triangle?

• All sides are equal

• At least two sides are congruent

• All angles are equal

• It has one right angle

If two sides of an isosceles triangle are congruent, what can be said about the angles opposite these sides?

• They are right angles

• They are complementary

• They are supplementary

• They are congruent

How do you solve for x in the equation 4x + 3 = 2x + 29?

• Add 2x to both sides

• Subtract 3 from both sides

• Subtract 2x from both sides

• Multiply both sides by 2

What is the value of x when 2x = 26?

• 39

• 26

• 13

• 52

What equation is set up to solve for y when the angles are congruent?

• 3y - 2 = 41

• 3y + 2 = 41

• 3y + 2 = 39

• 3y - 2 = 39

What is the value of y when 3y = 39?

• 15

• 13

• 12

• 10

In the second example, what is the sum of the interior angles of a triangle?

• 360 degrees

• 270 degrees

• 90 degrees

• 180 degrees

How do you find the measure of each base angle when the sum of the two base angles is 152 degrees?

• Multiply by 2

• Subtract 28

• Divide by 2

• Add 28

What is the equation to solve for x in the second example?

• 5x + 1 = 152

• 5x - 1 = 76

• 5x + 1 = 76

• 5x - 1 = 152

What is the value of x when 5x = 75?

• 10

• 20

• 12

• 15