Geometry Chapter 8 Test: Ratios and Means

Questions and Answers

What is the ratio of 3 inches to 4 feet?

1:16

What is the ratio of x to y if 2x = 5y?

5:2

What is the ratio of x to y if 6/x + 9 = 2/y + 3?

3:1

What is the geometric mean of 20 and 5?

+- 10 Signup and view all the answers

What is the geometric mean of 48 and 3?

+- 12 Signup and view all the answers

What is the geometric mean for 2 and 32?

+- 8 Signup and view all the answers

If a school's 50-foot flagpole casts a 75-foot shadow, how long will the shadow be for a 5-foot tall girl standing near the flagpole?

7.5 Signup and view all the answers

If A/x = Y/B, what are the means and extremes?

m = x, y; e = a, b Signup and view all the answers

If triangle HCS is similar to triangle PLD, what is HC/HS equal to?

PL/PD Signup and view all the answers

If DO IT = GO ON, what is GO/IT equal to?

DO/ON Signup and view all the answers

If triangle CAT is similar to triangle DOG and angle C = 70, angle T = x + 12, angle D = 7x, find angle T.

T = 22 Signup and view all the answers

What are the four ways to prove triangles similar?

AAA~, AA~, SAS~, SSS~ Signup and view all the answers

Study Notes

Ratios

The ratio of 3 inches to 4 feet is calculated as 1:16.
To find the ratio of x to y from the equation 2x = 5y, the ratio simplifies to 5:2.
When the equation ( \frac{6}{x} + 9 = \frac{2}{y} + 3 ) is solved, the ratio of x to y is 3:1.

Geometric Mean

The geometric mean of 20 and 5 is ±10.
For the numbers 48 and 3, the geometric mean is ±12.
The geometric mean for 2 and 32 is ±8.

Proportional Relationships

A 50-foot flagpole casts a 75-foot shadow; therefore, a 5-foot tall girl will cast a 7.5-foot shadow.
In the proportion ( \frac{A}{x} = \frac{Y}{B} ), the means are x and Y, while the extremes are A and B.
For similar triangles, if triangle HCS is similar to triangle PLD, then the ratio ( \frac{HC}{HS} ) equals ( \frac{PL}{PD} ).

Algebraic Equivalence

Given ( DOIT = GOON ), the ratio ( \frac{GO}{IT} ) translates to ( \frac{DO}{ON} ).

Angle Relationships in Similar Triangles

For similar triangles CAT and DOG, with angle C = 70 degrees, angle T expressed as ( x + 12 ), and angle D as ( 7x ), angle T can be calculated to be 22 degrees.

Triangle Similarity Criteria

Four methods to prove triangle similarity include AAA~, AA~, SAS~, and SSS~.

Description

This quiz covers key concepts from Chapter 8 of Geometry, focusing on ratios and geometric means. Join us to test your understanding of how to find ratios between different measurements and calculate geometric means. Perfect for reviewing important geometric principles!