Finals REVIEW - part 3 Fall 2024

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle.

Front

What is the triangle inequality theorem?

Back

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Can a triangle have sides of lengths 3, 4, and 9?

Back

No, because 3 + 4 is not greater than 9, violating the triangle inequality theorem.

Front

How do you solve for x in an equation?

Back

To solve for x, isolate x on one side of the equation using inverse operations (addition, subtraction, multiplication, division) to simplify the equation.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, which can be proven using criteria such as SSS, SAS, ASA, AAS, or HL.

Front

What is the significance of the notation ∆ABC≅∆XYZ?

Back

This notation indicates that triangle ABC is congruent to triangle XYZ, meaning their corresponding sides and angles are equal.

Front

What is the formula for finding the length of a side in a right triangle?

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 definition of a median in a triangle?

Back

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

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

What does it mean for two angles to be complementary?

Back

Two angles are complementary if the sum of their measures is 90 degrees.