STAAR Review Proportionality and Similar Figures TEKS 7.5 ABC

Front

What is the definition of \( \pi \)?

Back

The ratio of the circumference of a circle to its diameter.

Front

What is the formula for the circumference of a circle?

Back

The circumference \( C \) is given by \( C = \pi d \) or \( C = 2\pi r \), where \( d \) is the diameter and \( r \) is the radius.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

How do you find the scale factor between two similar figures?

Back

The scale factor is found by dividing the length of a side of one figure by the length of the corresponding side of the other figure.

Front

What is the relationship between the areas of two similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.

Front

If the scale factor of two similar triangles is 3:2, what is the ratio of their areas?

Back

The ratio of their areas is \( \left(\frac{3}{2}\right)^2 = \frac{9}{4} \).

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio or rate.

Front

How can you determine if two ratios are proportional?

Back

Two ratios are proportional if the cross products are equal, meaning \( a/b = c/d \) if and only if \( a \cdot d = b \cdot c \).

Front

What is the formula for the area of a circle?

Back

The area \( A \) of a circle is given by \( A = \pi r^2 \), where \( r \) is the radius.

Front

What is the definition of a ratio?

Back

A ratio is a comparison of two quantities by division, expressed as \( a:b \) or \( \frac{a}{b} \).