Exploring Isosceles and Equilateral Triangles

This video tutorial covers geometry concepts focusing on isosceles and equilateral triangles. It explains the properties of isosceles triangles, including the legs, base, and angles, and introduces the isosceles triangle theorem and its converse. The video also discusses equilateral triangles, highlighting the corollaries that equilateral triangles are also equiangular and vice versa. Practical applications of these theorems are demonstrated through problem-solving exercises, emphasizing the relationship between congruent sides and angles.

What is the name of the two congruent sides in an isosceles triangle?

• Hypotenuse

• Vertex

• Legs

• Base

In an isosceles triangle, what is the name of the angle opposite the base?

• Vertex angle

• Supplementary angle

• Right angle

• Base angle

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

• They are right angles

• They are supplementary

• They are complementary

• They are congruent

What does the isosceles triangle converse theorem state?

• If two angles are congruent, the sides opposite them are congruent

• If two angles are congruent, the triangle is right-angled

• If two sides are congruent, the triangle is equilateral

• If two sides are congruent, the angles opposite them are supplementary

What is true about the angles in an equilateral triangle?

• They are all 30 degrees

• They are all 90 degrees

• They are all 60 degrees

• They are all 45 degrees

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

• They are all different lengths

• Two sides are equal

• One side is longer than the other two

• All three sides are equal

How can you determine the measure of each angle in an equilateral triangle?

• Divide 180 by 2

• Divide 360 by 2

• Divide 180 by 3

• Divide 360 by 3

If the measure of one angle in an isosceles triangle is 120 degrees, what is the measure of each of the other two angles?

• 45 degrees

• 90 degrees

• 60 degrees

• 30 degrees

Given two congruent sides in a triangle, how can you find the measure of the base angles?

• Subtract the base angles from 180

• Subtract the vertex angle from 180 and divide by 2

• Divide the vertex angle by 2

• Add the base angles and divide by 2

If two sides of a triangle are congruent and one of the base angles is 50 degrees, what is the measure of the other base angle?

• 80 degrees

• 50 degrees

• 70 degrees

• 60 degrees