Properties of Right Triangles

The video tutorial covers the inscribed right triangle theorem, explaining that if a right triangle is inscribed in a circle, its hypotenuse is the diameter. It discusses how to determine arc measures and semicircles, using examples to solve for angles in inscribed triangles. The tutorial also includes an example of an isosceles right triangle, demonstrating how to solve for unknown variables.

What is the relationship between the hypotenuse of an inscribed right triangle and the circle?

• The hypotenuse is a chord of the circle.

• The hypotenuse is a tangent to the circle.

• The hypotenuse is the diameter of the circle.

• The hypotenuse is the radius of the circle.

What is the measure of angle G in the inscribed right triangle?

• 45 degrees

• 60 degrees

• 90 degrees

• 120 degrees

If a right triangle is inscribed in a circle, what is the measure of the arc opposite the right angle?

• 90 degrees

• 360 degrees

• 270 degrees

• 180 degrees

What is the measure of arc FJH in the inscribed right triangle?

• 90 degrees

• 120 degrees

• 150 degrees

• 180 degrees

In the example problem, what is the sum of angles F and H in the inscribed right triangle?

• 120 degrees

• 90 degrees

• 60 degrees

• 45 degrees

How do you solve for angle F in the given example problem?

• By measuring the arc directly.

• By using the Pythagorean theorem.

• By using trigonometric ratios.

• By setting up an equation with the sum of angles in a triangle.

What type of triangle is used in the second example problem?

• Isosceles right triangle

• Scalene triangle

• Equilateral triangle

• Obtuse triangle

In the second example, what are the measures of the two congruent angles in the isosceles right triangle?

• 60 degrees

• 90 degrees

• 45 degrees

• 30 degrees

What equation is set up to solve for X in the second example problem?

• 50 = 2x

• 3x + 5 = 2x

• 3x - 5 = 2x

• 35 = 2x

What is the value of X in the second example problem?

• 25

• 20

• 15

• 10