Flashcard - 6.1-6.2 Ratios, Proportions, Sides of Similar Triangles

Front

What is a similarity statement for triangles?

Back

A similarity statement indicates that two triangles are similar, meaning their corresponding angles are equal and their corresponding sides are in proportion. Example: ΔABC ~ ΔDEF.

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. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

How do you find the missing side in similar triangles?

Back

To find the missing side in similar triangles, set up a proportion using the lengths of the corresponding sides of the triangles.

Front

What is the formula for the ratio of corresponding sides in similar triangles?

Back

The ratio of corresponding sides in similar triangles is equal to the ratio of their corresponding altitudes, medians, and other segments.

Front

If ΔYZX ~ ΔNWE, what can we conclude about their angles?

Back

If ΔYZX ~ ΔNWE, then angle Y = angle N, angle Z = angle W, and angle X = angle E.

Front

What is the value of x if the corresponding sides of two similar triangles are in the ratio 2:5 and one side is 4?

Back

If the ratio is 2:5 and one side is 4, then x = 10 (4 * 5/2).

Front

How do you solve for x in a proportion?

Back

To solve for x in a proportion, cross-multiply and then isolate x. For example, if a/b = c/d, then ad = bc.

Front

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

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Front

If two triangles are similar and one has a side length of 6 and the other has a corresponding side length of 9, what is the scale factor?

Back

The scale factor is 6:9 or 2:3.

Front

What is the significance of corresponding angles in similar triangles?

Back

Corresponding angles in similar triangles are equal, which is a key property that helps establish similarity.