Exploring Isosceles and Equilateral Triangles

If segment AB is congruent to segment BC in a triangle, which angles are congruent?

• Angle ACB and Angle ABC

• Angle BAC and Angle BCA

• Angle ABC and Angle BAC

• Angle ACB and Angle BAC

What is the converse of the isosceles triangle theorem?

• If a triangle has a right angle, then it is a right triangle.

• If a triangle is equilateral, then all angles are 60 degrees.

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

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

In the example with the architect designing a park, if one angle is 50 degrees, what are the measures of the other two angles?

• 65 degrees each

• 50 degrees each

• 60 degrees each

• 70 degrees each

Using the isosceles triangle theorem, if the total degrees in a triangle is 180 and one angle is 50 degrees, what is the equation to find the other two angles?

• 180 = 50 + x + x

• 180 = 50 + 2x

• 180 = 50 + x

• 180 = 2x + 50

When solving for side lengths using the converse of the isosceles triangle theorem, what equation would you set up if X + 20 equals 8X divided by 3?

• 3(X + 20) = 8X

• 3X + 20 = 8X

• X + 20 = 8X / 3

• X + 20 = 3(8X)

If a line bisects the vertex angle of an isosceles triangle, what does it also bisect?

• The opposite side at a 90-degree angle

• The base angles

• The entire triangle

• The hypotenuse

In the example with the prefabricated house, what theorem is used to determine if the house can pass under a 17-foot bridge?

• Isosceles triangle theorem

• Converse of the isosceles triangle theorem

• Equilateral triangle theorem

• Pythagorean theorem

What is the height of the house if the roof height is 7.75 feet and the house height is 10 feet?

• 16.75 feet

• 18 feet

• 17 feet

• 17.75 feet

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

• 120 degrees

• 90 degrees

• 60 degrees

• 45 degrees

If an equilateral triangle has all sides congruent, what can be said about its angles?

• One angle is 90 degrees

• Two angles are congruent

• All angles are different

• All angles are congruent