Gr12 Mathematics: Ch 7.1 Ratio and Proportion

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What is the primary purpose of a ratio?

To compare quantities with different units
To provide the actual measurements of quantities
To simplify complex calculations
To express how many times one quantity is contained in the other (correct)

If two ratios are equal, what can be said about the quantities involved?

They have different values
They are not proportional
They have the same units
They are in proportion (correct)

What is the property of proportion that states wx = xy?

Alternating Proportion
Reciprocal Proportion
Inverted Proportion
Cross Multiplication (correct)

What theorem states that a line drawn parallel to one side of a triangle divides the other two sides proportionally?

Basic Proportionality Theorem (C), Thales' Theorem (D) Signup and view all the answers

What is the first step in solving proportional problems?

Identify the given ratios (C) Signup and view all the answers

What is a key point to remember when working with ratios?

Ratios should be simplified to their simplest form (C) Signup and view all the answers

What is the purpose of proportions in geometry?

To compare different parts of geometric figures (B) Signup and view all the answers

What is the result of cross-multiplying two ratios?

The product of the numerator of one ratio and the denominator of the other is equal to the product of the denominator of one ratio and the numerator of the other (B) Signup and view all the answers

Which of the following is a key characteristic of a ratio?

Ratios are unit-less because they compare quantities of the same kind. (C) Signup and view all the answers

If $rac{a}{b} = rac{c}{d}$, which of the following is true?

$a \cdot d = b \cdot c$ and $a \cdot c = b \cdot d$ (C) Signup and view all the answers

In a triangle, if a line is drawn parallel to one side, what can be said about the other two sides?

They are divided proportionally. (C) Signup and view all the answers

What is the purpose of setting up proportional equations when solving proportional problems?

To establish a relationship between the quantities. (B) Signup and view all the answers

If $rac{a}{b} = rac{c}{d}$, which of the following is also true?

$rac{b}{a} = rac{d}{c}$ (D) Signup and view all the answers

What is the result of inverting a proportion?

The ratios are swapped. (C) Signup and view all the answers

Which of the following is an example of a proportional theorem?

Basic Proportionality Theorem (C) Signup and view all the answers

What is the benefit of using ratios and proportions in geometry?

They help compare different parts of geometric figures. (C) Signup and view all the answers

In a triangle, if a line is drawn parallel to one side, what is the relationship between the divided segments?

They are proportional (A) Signup and view all the answers

If $\frac{a}{b} = \frac{c}{d}$, which of the following is NOT a property of proportion?

Linear Proportion (C) Signup and view all the answers

What is the purpose of simplifying ratios?

To express the ratio in its simplest form (A) Signup and view all the answers

If $\frac{w}{x} = \frac{y}{z}$, which of the following is true?

$wx = xy$ (A) Signup and view all the answers

What is the benefit of using proportions in geometry?

It helps to compare different parts of geometric figures (B) Signup and view all the answers

If $\frac{a}{b} = \frac{c}{d}$, which of the following is true?

$\frac{b}{a} = \frac{d}{c}$ (D) Signup and view all the answers

What is the primary purpose of identifying given ratios when solving proportional problems?

To determine which quantities are being compared (C) Signup and view all the answers

Which of the following is an example of a proportional theorem in geometry?