Angles and Lengths of Isosceles and Equilateral Triangles

The video tutorial covers the properties and problem-solving techniques for isosceles and equilateral triangles. It explains the characteristics of these triangles, provides examples of how to solve related problems, and highlights the presence of isosceles triangles in circles. The tutorial also offers tips for identifying these triangles in various contexts, such as standardized tests like the ACT.

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

• 120°

• 90°

• 60°

• 45°

Which of the following is true about isosceles triangles?

• All sides are equal

• No sides are equal

• All angles are equal

• Two sides are of equal length

In an isosceles triangle, if side AB equals side AC, which angles are equal?

• Angle B and Angle C

• None of the angles are equal

• Angle A and Angle C

• Angle A and Angle B

Given an isosceles triangle ABC with AB = BC and height BD, if angle A is 40° and angle D is 90°, what is the value of angle B?

• 30°

• 60°

• 40°

• 50°

In a circle, if a triangle has two vertices on the circumference and one vertex at the center, what type of triangle is it?

• Equilateral

• Right-angled

• Scalene

• Isosceles

If AO and BO are radii of a circle and form a triangle with point A and B on the circumference, what can be said about the triangle?

• It is an isosceles triangle

• It is a right-angled triangle

• It is a scalene triangle

• It is an equilateral triangle

In a triangle with vertices A, B, and O, if AO and BO are radii of the circle and angle AOB is 85°, what is the measure of the other two angles?

• 47.5° each

• 85° each

• 60° each

• 90° each

If the sum of the interior angles of a triangle is 180°, what is the missing angle in a triangle where two angles are 85° each?

• 10°

• 20°

• 30°

• 40°

What is the measure of angle AOB if it is greater than 180° and the other angles are 10°, 115°, and 60°?

• 185°

• 175°

• 205°

• 195°

If angle AOB is less than 180° and the other angles are 10°, 115°, and 60°, what is the measure of angle AOB?

• 180°

• 175°

• 170°

• 165°