Topics in High School Geometry Curriculum
Area:
The area may be defined as the quantity that is used to expresses the extent of a two-dimensional region, shape, in the plane. In the case of two dimensions and three dimensions, the area is analogous to the surface area.
Angles
Angle is formed at a point of intersection of two lines or rays. The angle may be formed by the intersection of two planes too. The angle is the measure of the turn between two lines or two planes.
Points
A point in geometry is a method to show a location. Point is a dimensionless quantity as it has no size, no width, no length, and no depth. A point is represented by a dot. A line is defined as a line of points that extends infinitely in two directions and points that lie on the same line are called collinear points.
Planes
In mathematics, a plane is defined as a flat and two-dimensional surface that extends infinitely. A plane is the two-dimensional analog of a point (0 dimensions), a line (1D), and 3D space.
Lines
In mathematics/geometry, a line may be defined as a straight 1D figure that has no thickness and extends endlessly in both directions and is often described as the shortest distance between any two points.
Circles
A circle looks like a round-shaped figure that has no corners and has no edges. In mathematics/geometry, a circle may be defined as a closed, two-dimensional curved shape in which all the points on the cure are at a fixed distance from a point. This point is known as the center of a circle. This fixed distance from the center to the point on the curve is known as the radius of the circle.
Polygons
In mathematics/geometry, a polygon is a plane figure that has a finite number of straight-line segments having a closed shape. The polygons do not have any curved sides i.e. all the lines are straight. Triangle is an example of the three-sided polygon. Similarly, four, five, six-sided polygon are called quadrilateral, pentagon, hexagon respectively.
Triangles
Triangle may be defined as a three-sided polygon, i.e. It has three sides and three angles are formed at the intersection of three sides.
Transformations
In mathematics, transformation may be defined as the process of converting a single form from one domain to another. The signal can be transformed from the time domain to the frequency domain or vice versa by using various transformation methods like Laplace Transformation, Fourier Transformation, etc.
Quadrilaterals
Quadrilaterals may be defined as polygons having four sides. It has four angles. Square, rectangle, rhombus are examples of the quadrilateral.
Similarity
In geometry, the similarity is the property when two figures are identical to each other.
Coordinate Geometry
Coordinate geometry is also known as analytic geometry may be defined as the study of geometry by making use of coordinate points. By using the coordinate geometry, we can find the distance between two points, dividing lines in the x:y ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc.
Right triangles
A triangle may be termed as a right-angled triangle if one angle of the triangle is 90 degrees. The side opposite to the right angle in the right triangle is called hypotenuse and the remaining two sides are known as base and perpendicular.
Trigonometry
Trigonometry may be defined as a branch of mathematics that studies relationships between side lengths and angles of triangles by making use different trigonometric relationships on the triangle.
Perpendicular and parallel
Two lines are said to be perpendicular if the angle between them is 90 degrees at the point of intersection whereas if two lines don't intersect with each other at any point even after infinite expansion at both ends, then the line is said to be a parallel line.
Sample High School Geometry Problems
Q1. What is the exterior angle of the regular octagon?
Sol. Regular octagon have all angles equals
And by exterior angle sum property of polygons,
We have sum of all the exterior angle equals to 360°
So, 8×exterior angle=360°
exterior angle= 360°8
exterior angle= 45°
Q2. Find the arc length of a circle with radius 14 cm making an angle of 36° at the centre.
Sol. Radius of the = 14 cm
Angle at the centre = 36°
Arc length = e/360.2πr
= 36/360× 2× 22/7×14
= 8.8 cm
Q3. Find if the following triangles are congruent or not, If the two sides are equal.
Lets imagine one triangle as ABC and other as PQR
Sol. We have
AB = PQ ( from figure )
BC = QR ( from figure )
∠B = ∠Q ( from figure )
So, by side angle side congruency rule we have
∆ABC≅∆PQR
Get Timely Solutions to High School Geometry Problems!
Geometry is the oldest branch of Mathematics. For high school graduates taking at least three years of math, including algebra and geometry, is a minimum requirement. The typical course order is::
Geometry is usually taken in a student’s 2nd year of high school. The high school geometry curriculum introduces students to the concepts of basic trigonometry, angles of elevation and depression, and methods of proving triangle congruence.
If you are looking to be admitted to a good university or college after high school, then focusing on Geometry is very important. The University of California among other requirements asks students to study two- and three-dimensional geometry in order to get admission at the prestigious university.
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What is a plane in geometry?
A two-dimensional flat surface that extends upto infinity and far is called a plane in geometry. It’s a figure that has no thickness and extends infinitely in two directions.
Length and width are the two dimensions of a plane.
What is a ray in geometry?
A line that has a fixed starting point but extends indefinitely is called a ray in geometry. A ray extends infinitely in one direction but has a single point of origin. For instance: rays emitted from the Sun extend in one direction only.
What is a line in geometry?
A collection of points along a straight path is called a line. It’s a one dimensional figure that has no width but only length. A line also extends in both directions infinitely.
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What are the basics of geometry?
Point, line and plane are regarded as the basic concepts of geometry. To learn the fundamentals in the subject, you must also know:
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