PRAXIS II Mathematics Content Knowledge Exam Prep

A circle is a closed shape with no corners or edges. It is formed by a set of points that are equidistant from a fixed center point. The total angle obtained in a circle is 360°. This is because a circle is composed of 360 degrees, which means that if you were to travel along the circumference of a circle, you would have traveled 360 degrees. Therefore, the correct answer is 360°.

A quadrilateral is a polygon with four sides. A triangle, on the other hand, is a polygon with three sides. Therefore, a triangle is not a quadrilateral because it does not have four sides.

A confidence interval is not a numerical descriptor because it is a range of values that is used to estimate an unknown population parameter, such as the mean or proportion. It is not a single value that describes a specific characteristic of the data set. In contrast, the median, standard deviation, and mean are all numerical descriptors that provide information about the central tendency, variability, and average of a set of numerical data.

The term "congruents" does not refer to any specific part of a triangle. Congruent refers to two figures that have the same shape and size. In the context of a triangle, congruence would refer to two triangles that are identical in shape and size. However, congruents itself is not a part of a triangle, unlike opposite, adjacent, and hypotenuse which are all terms used to describe specific parts or relationships within a triangle.

The Law of reciprocals is alien to trigonometry because it is not a recognized principle or formula in trigonometry. The other three options, Law of tangents, Law of sines, and Law of cosines, are well-known laws that are commonly used in trigonometry to solve various problems involving angles and sides of triangles. However, the Law of reciprocals is not a standard concept in trigonometry and is not commonly used in calculations or problem-solving.

Euclidean geometry is the correct answer because it is the branch of mathematics that deals with the properties and relationships of points, lines, angles, and shapes in a flat space. It is the most well-known and traditional form of geometry, developed by the ancient Greek mathematician Euclid. Differential geometry, topology, and convex geometry are all different branches of geometry that focus on specific aspects or applications, but they are not synonymous with classical geometry.

Perimeter is not a geometrical element because it is a measurement of the distance around the boundary of a two-dimensional shape. Geometrical elements typically refer to the fundamental components of shapes, such as lines, points, angles, and surfaces. Perimeter is a derived quantity that depends on the shape and size of an object, rather than being an inherent element of geometry.

A quadrilateral is a polygon with four sides. The sum of the internal angles in any quadrilateral is always equal to 360°. Therefore, none of the given answer choices of 180°, 120°, or 100° can be correct. The only option that is close to the correct answer is 90°, but it is not the correct answer.

Slopians is not a measurement method for angles. Radians, degrees, and gradians are all valid measurement methods for angles. Radians measure angles based on the radius of a circle, degrees measure angles based on a circle divided into 360 equal parts, and gradians measure angles based on a circle divided into 400 equal parts. However, there is no such measurement method called "slopians" for measuring angles.

Sextants are navigational instruments used to measure the angles between celestial objects, such as stars or the sun, and the horizon. Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles. In the case of sextants, trigonometry is used to calculate the distance between the observer and the celestial object based on the measured angles. Therefore, trigonometry is the mathematical principle that governs sextants.