Str. & Shr. Flashcard 2 - Inv. 3

Front

What is the definition of similar triangles?

Back

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

Front

How do you find the length of a side in similar triangles?

Back

To find the length of a side in similar triangles, set up a proportion using the lengths of corresponding sides from the two triangles and solve for the unknown length.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if they satisfy one of the following conditions: 1) AA (Angle-Angle) criterion: two angles of one triangle are equal to two angles of another triangle; 2) SSS (Side-Side-Side) criterion: the sides of one triangle are proportional to the sides of another triangle; 3) SAS (Side-Angle-Side) criterion: two sides of one triangle are proportional to two sides of another triangle, and the included angle is equal.

Front

What is the significance of the ratio of the sides in similar triangles?

Back

The ratio of the sides in similar triangles is constant and is equal to the ratio of any pair of corresponding sides.

Front

How can you find an unknown angle in similar triangles?

Back

To find an unknown angle in similar triangles, use the fact that the sum of the angles in a triangle is 180 degrees and that corresponding angles in similar triangles are equal.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

What is the relationship between the sides of a right triangle and the angles?

Back

In a right triangle, the side opposite the largest angle (the right angle) is the hypotenuse, and the lengths of the other two sides are related to the angles through trigonometric ratios.

Front

How do you calculate the height of a triangle given the area and base?

Back

To calculate the height of a triangle given the area and base, use the formula: height = (2 * Area) / base.