Exploring Isosceles and Equilateral Triangles

Mr. Truman's geometry lesson covers the properties and theorems of isosceles and equilateral triangles. He explains how to identify these triangles, their congruent sides and angles, and how to apply these properties to solve problems. The lesson includes examples of solving for unknowns in isosceles triangles and calculating the height of equilateral triangles using the Pythagorean theorem.

What is the defining property of an isosceles triangle?

• All sides are equal

• Two sides are congruent

• All angles are equal

• It has a right angle

In an isosceles triangle, if two sides are congruent, what can be said about the base angles?

• They are different

• They are congruent

• They are right angles

• They are obtuse

If an isosceles triangle has base angles of 30 degrees each, what is the measure of the vertex angle?

• 150 degrees

• 120 degrees

• 90 degrees

• 60 degrees

Given an isosceles triangle with sides 8x and 4x + 5, how do you solve for x?

• Set 8x equal to 4x + 5 and solve

• Set 8x equal to 4x - 5 and solve

• Set 8x equal to 5 and solve

• Set 4x equal to 5 and solve

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

• 90 degrees

• 60 degrees

• 120 degrees

• 45 degrees

If all sides of an equilateral triangle are equal, what can be said about its angles?

• They are all different

• They are all right angles

• They are all congruent

• They are all obtuse

In an equilateral triangle, if one angle is 60 degrees, what are the measures of the other two angles?

• 90 degrees each

• 45 degrees each

• 60 degrees each

• 120 degrees each

How do you find the height of an equilateral triangle with side length 12 using the Pythagorean theorem?

• Divide the side length by 3 and use it as the base

• Divide the side length by 2 and use it as the base

• Divide the side length by 4 and use it as the base

• Use the side length directly as the height

What is the approximate height of an equilateral triangle with side length 12?

• 12.0

• 10.4

• 8.0

• 6.0

Which theorem is used to find the height of an equilateral triangle?

• Pythagorean Theorem

• Triangle Sum Theorem

• Congruent Triangles Theorem

• Base Angles Theorem