12-6 Triangle Proportionality Practice

Front

What is the Triangle Proportionality Theorem?

Back

If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

The lengths of corresponding sides are proportional.

Front

What is the formula for finding the length of a missing side in similar triangles?

Back

If triangles are similar, then \( \frac{a}{b} = \frac{c}{d} \), where a and b are corresponding sides of one triangle, and c and d are corresponding sides of the other.

Front

How do you determine if two segments are parallel using ratios?

Back

If the ratios of the lengths of the segments are equal, then the segments are parallel.

Front

What does it mean for two ratios to be equal?

Back

Two ratios are equal if they represent the same fraction or proportion.

Front

If \( a = 6 \) and \( b = 12 \), what is the ratio \( \frac{a}{b} \)?

Back

The ratio \( \frac{a}{b} = \frac{6}{12} = \frac{1}{2} \).

Front

What is the significance of parallel lines in triangle proportionality?

Back

Parallel lines create similar triangles, allowing for the use of proportionality to find missing lengths.

Front

If two triangles have sides of lengths 3, 4, and 5, and 6, 8, and 10, are they similar?

Back

Yes, because the ratios of corresponding sides are equal: \( \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{1}{2} \).

Front

What is the first step in solving for a missing length in a triangle?

Back

Identify the corresponding sides and set up a proportion.

Front

If \( x \) is the missing length in a triangle with sides 5 and 10, what is \( x \) if the corresponding side is 20?

Back

Using the proportion \( \frac{5}{10} = \frac{x}{20} \), we find \( x = 10 \).