Triangle Proportionality/Similarity Applications Review

Front

What is the Triangle Proportionality Theorem?

Back

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

Define similar triangles.

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the formula for finding the height of an object using similar triangles?

Back

The height can be found using the proportion: \( \frac{height_1}{shadow_1} = \frac{height_2}{shadow_2} \) where height_1 and shadow_1 are for one object, and height_2 and shadow_2 are for the other.

Front

If a ladder is leaning against a wall, how can you find the height it reaches?

Back

Use the Pythagorean theorem: if the ladder length is \( c \) and the distance from the wall is \( a \), then height \( b \) can be found using \( b = \sqrt{c^2 - a^2} \).

Front

What is the relationship between the lengths of the sides of similar triangles?

Back

The lengths of the corresponding sides of similar triangles are proportional.

Front

How do you set up a proportion to solve for a missing length in similar triangles?

Back

Set up the proportion using corresponding sides: \( \frac{side_1}{side_2} = \frac{missing\,length}{known\,length} \).

Front

What is the significance of the shadow length in problems involving similar triangles?

Back

The shadow length can be used to create proportions that help find unknown heights or lengths of objects.

Front

How can you determine the height of a tree using the shadow of a person?

Back

Use the proportion: \( \frac{height_{tree}}{shadow_{tree}} = \frac{height_{person}}{shadow_{person}} \).

Front

What is the formula for the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.

Front

What does it mean for two triangles to be in proportion?

Back

Two triangles are in proportion if the ratios of their corresponding sides are equal.