Geometry Chapter 9 Quiz

Questions and Answers

What do special right triangles refer to?

Triangles with obtuse angles

45-45-90 and 30-60-90 triangles (correct)

Triangles with equal sides

Isosceles triangles

How do you find the hypotenuse in a 45-45-90 triangle?

hypotenuse = leg x √2

How do you find the hypotenuse in a 30-60-90 triangle?

hypotenuse = shortest leg x 2

How do you find the longest leg of a 30-60-90 triangle?

longest leg = shortest leg x √3 Signup and view all the answers

What is Theorem 9.8 (45-45-90 Theorem)?

In a 45-45-90 triangle, the hypotenuse is √2 times as long as each leg. Signup and view all the answers

What is Theorem 9.9 (30-60-90 Theorem)?

In a 30-60-90 triangle, the hypotenuse is twice as long as the shortest leg and the longer leg is √3 times as long. Signup and view all the answers

What are trigonometric ratios?

Ratios that help solve side lengths of right triangles. Signup and view all the answers

What does SOHCAHTOA stand for?

SIN/sine (Opposite/Hypotenuse), COS/cosine (Adjacent/Hypotenuse), TAN/tangent (Opposite/Adjacent) Signup and view all the answers

What does it mean to solve a right triangle?

The process of determining all 6 measurements within a right triangle (3 side lengths, 3 angle measures). Signup and view all the answers

Study Notes

Special Right Triangles

Includes two types of triangles: 45-45-90 and 30-60-90.
Known for consistent relationships among their side lengths.

45-45-90 Triangle

Hypotenuse can be calculated using the formula: hypotenuse = leg x √2.

30-60-90 Triangle

Hypotenuse is found using: hypotenuse = shortest leg x 2.
The longest leg (2nd longest side) can be determined as: longest leg = shortest leg x √3.

Theorems

Theorem 9.8 (45-45-90 Theorem): In this triangle, the hypotenuse measures √2 times the length of each leg.
Theorem 9.9 (30-60-90 Theorem): In this triangle, the hypotenuse is twice the length of the shortest leg, while the longer leg equals √3 times the shortest leg.

Trigonometric Ratios

Essential for calculating side lengths in right triangles.

SOHCAHTOA

A mnemonic to remember trigonometric functions:
- SIN (sine): Opposite/Hypotenuse
- COS (cosine): Adjacent/Hypotenuse
- TAN (tangent): Opposite/Adjacent

Solving a Right Triangle

Involves calculating all six measurements: three side lengths and three angle measures.

Description

Test your knowledge on special right triangles with this quiz. Explore the relationships between side lengths in 45-45-90 and 30-60-90 triangles. Learn how to find the hypotenuse and longest leg with ease.