Hon. Geom. FLASHCARD REVIEW Unit 5

Front

What is the formula to find the length of a side in a triangle using the centroid?

Back

The centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Front

Define the centroid of a triangle.

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the center of mass of the triangle.

Front

What are medians in a triangle?

Back

Medians are line segments that connect a vertex of the triangle to the midpoint of the opposite side.

Front

How do you find the length of a side in a triangle if two sides are known?

Back

You can use the Pythagorean theorem if the triangle is right-angled, or apply the law of cosines for other types of triangles.

Front

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

Back

In a triangle, the larger the angle, the longer the opposite side; conversely, the smaller the angle, the shorter the opposite side.

Front

What is the significance of the centroid in triangle geometry?

Back

The centroid is the balance point of the triangle and divides each median into a 2:1 ratio.

Front

How do you calculate the area of a triangle given the lengths of its sides?

Back

You can use Heron's formula: Area = √[s(s-a)(s-b)(s-c)], where s is the semi-perimeter (s = (a+b+c)/2).

Front

What is the semi-perimeter of a triangle?

Back

The semi-perimeter is half the sum of the lengths of the triangle's sides, calculated as s = (a+b+c)/2.

Front

What is the formula for the area of a triangle using base and height?

Back

Area = 1/2 * base * height.

Front

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

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and the lengths of the other two sides can be found using the Pythagorean theorem.