Understanding 30-60-90 Triangles

This video tutorial discusses 30-60-90 triangles, focusing on their angle measures and the ratios between their sides. The instructor begins by explaining the significance of these triangles in geometry and trigonometry. An equilateral triangle is constructed, and an altitude is dropped to form two 30-60-90 triangles. The video demonstrates how to prove the side ratios using congruence postulates and the Pythagorean theorem, showing that the side opposite the 30-degree angle is half the hypotenuse, and the side opposite the 60-degree angle is the square root of 3 times half the hypotenuse.

What are the angle measures of a 30-60-90 triangle?

• 30, 60, and 90 degrees

• 45, 45, and 90 degrees

• 60, 60, and 60 degrees

• 90, 90, and 90 degrees

If the hypotenuse of a 30-60-90 triangle is x, what is the length of the side opposite the 30-degree angle?

• x√3

• x√3/2

• x/2

• x

What is the length of the side opposite the 60-degree angle in a 30-60-90 triangle if the hypotenuse is x?

• x√3

• x

• x√3/2

• x/2

What is a key property of an equilateral triangle?

• Two sides are equal

• One angle is 90 degrees

• All sides are equal

• All angles are 90 degrees

What happens when you drop an altitude in an equilateral triangle?

• All of the above

• It bisects the base

• It creates two right triangles

• It creates two congruent triangles

Which congruence postulate can be used to prove the congruence of two triangles formed by an altitude in an equilateral triangle?

• Angle-Side-Angle

• Angle-Angle-Side

• Side-Side-Side

• Side-Angle-Side

What is the length of the base segments when an altitude is dropped in an equilateral triangle of side x?

• x

• x√3/2

• x/2

• x√3

How do you find the length of the side opposite the 60-degree angle using the Pythagorean theorem?

• By subtracting the square of the shorter side from the hypotenuse squared

• By multiplying the hypotenuse by √3

• By dividing the hypotenuse by 2

• By adding the squares of the other two sides

What is the principal root of 3x squared over 4?

• x√3

• x√3/2

• x/2

• 3x/2

In a 30-60-90 triangle, if the hypotenuse is x, what is the length of the side opposite the 60-degree angle?

• x

• x/2

• x√3/2

• x√3