GMAT Geometry Syllabus 2020: Section Wise Details
The GMAT exam is a universally accepted exam for which students study day and night to secure a chance in one of the reputed business schools. GMAT syllabus comprises an array of genres like verbal reasoning, analytical writing assessment, quantitative analysis, and logical reasoning. Each section consists of distinct headings to cover. Test-takers are always advised to start their preparation almost four months beforehand. GMAT exam’s difficulty level is not tremendously hard but its nature is tricky. This means, students mostly fall behind when it comes to coping with their nervousness while solving the questions which are portrayed very confusingly. All these are majorly faced in either GMAT Quant or GMAT Verbal Reasoning section. But the main problem arises out of the heedlessness about the syllabus that the students suffer from. In the quant section of GMAT, there are numerous topics and every topic has its own way of handling the sums. Majorly the quant section is divided into GMAT arithmetic, GMAT geometry, and GMAT algebra.
The GMAT geometry syllabus is filled with different topics. Let us discuss the geometry portion in detail underneath.
GMAT Geometry: Lines
Let us start with this chapter from the GMAT geometry syllabus as this is the first step towards a complete study of GMAT quant. Lines are straight pathways that direct towards both directions.
- Parallel and intersecting lines: parallel lines run towards the same direction and never intersect each other. Whereas, intersecting lines are the ones that intersect at a point.
GMAT Geometry: Angles
When two straight lines conjunct at a point, they result in an angle. That point is termed as the vertex of the angle, and the lines are known as the sides of the angle. The size of an angle relies on the inclination of one side on the other. An angle is usually measured in degrees or radians. Syllabus for GMAT geometry’s angles include:
- Acute angle: has a measure of lower than 90 degrees and comprises of a sharp point,
- Right or perpendicular angle: measures exactly 90 degrees and portrays a square corner,
- Obtuse angle: this measures of more than 90 but less than 180 degrees and it is basically contrary to an acute angle and also looks dull,
- Straight angle: It measures 180 degrees,
- Complementary angle: when two angles totes up to 90 degrees,
- Supplementary angle: when two angles tote up to 180 degrees and this can be further explained through – similar: when objects are made up of similar shape but different sizes and congruent: objects equal in size and shape.
- Rules for lines and angles: intersecting lines and parallel lines intersected by traversal.
GMAT Geometry: Triangle
A triangle is a three-sided shape whose three inner angles must result in 180 degrees. The biggest angle will be crosswise from the longest side while the smallest angle will be crosswise from the trivial side of the triangle. If two sides of a triangle are similar, the angles contrary to them will be equivalent as well.
Properties of the triangle:
- the total of all the interior angles is 180 degrees,
- the conjoining of any two sides of a triangle must be bigger than the third side of a triangle,
- The lengthiest side of a triangle is opposite the largest angle of a triangle,
- An exterior angle of a triangle is equivalent to the sum of two remote interior angles.
Types of triangles:
- Scalene: It has no uniformity in its shape and sides,
- Isosceles: isosceles triangle has a minimum of two similar sides, and the parameters of the angles contrary to those two sides are also alike each other.
- Equilateral: this triangle has three sides of similar length and three 60 degree angles.
- Right angle: the right angle measures 90 degrees.
GMAT Geometry: Special Triangle
While doing triangles, students preparing for GMAT quant will learn another topic that is a special triangle. As we know that one of the angles of the right angle is 90 degrees. To form that 90 degrees, two special right angles are formed 45-45-90 and 30-60-90. The 45-45-90 is formed by separating the square and making it a diagonal and that is known as an isosceles right triangle. The 30-60-90 triangle is formed by cutting the equilateral triangle into half.
- Pythagorean Theorem: The Pythagorean Theorem states a mathematical relationship between the sides of a right triangle where the right triangle is any triangle that has one right internal angle. This one has always been a very vital chapter in the GMAT geometry syllabus.
- Pythagorean triplets
GMAT Geometry: Quadrilaterals
A quadrilateral is a four-sided polygon and is a very common topic in the GMAT quant. The addition of interior angles for all quadrilaterals has to be balanced with 360 degrees. GMAT Geometry syllabus for Quadrilaterals include
- Square: It is basically a rectangle consisting of balanced sides and thereby finding the area is quite effortless when we know one of its side’s length. Its features are – all sides are similar in length, all angles are right angles, the contrary sides are corresponding, Perimeter = 4 × (side) = 4 × L, Area = (Side) × (Side) = L × L = L2.
- Rectangle: A rectangle is a parallelogram with four sides. Its features include – opposite sides are similar in length and parallel in length, all angles are right angles, Perimeter = 2 × (Length + Breadth) = 2 × (L + B), Area = (Length) × (Breadth) = L × B.
- Parallelogram: its features include contrary sides which are identical in length and parallel, contrary angles which are balanced, adjacent angles are supplementary and the parameters of the adjacent angles adjoins up to 180 degrees, the diagonals bisect each other. In other words, they cross at the midpoint of both diagonals. Perimeter = 2 × (Length + Breadth) = 2 × (L + B)
- Rhombus: it has four equal sides but not certainly four right angles. It has features like - all sides are identical in length (all angles are not identical), adjacent angles are supplementary, opposite angles are equal, diagonals cut each other at right angles. Perimeter = 4 × (Side) = 4 × L, Area = (multiple of diagonals)/2 = ½d1d2
- Trapezoid: it is a quadrilateral with one set of parallel sides. Perimeter = Sum of sides = A + B + C + D, Area = (Height) × (Sum of parallel sides)/2 = (h) × (A + B)/2 = ½(b1 + b2)h.
GMAT Geometry: Circles
A circle can be defined as a set of points which are placed at an established distance from a mentioned point.
- Circumference and area of a circle: These are the formulas for finding the above points while solving GMAT geometry. It is to be noted that the diameter is two times the radius of the circle.
- Chord of the circle: any line segment which produces endpoints on the circle is called chords. And the chord that runs through the center of the circle is known as diameter.
- Arc of circle: an arc of a circle can be defined as a portion of a circle along the circumference.
- Tangent to a circle: when the tangent line touches the circle at a certain point it is then known tangent to the circle.
GMAT Geometry: Polygons
A polygon is a two-dimensional shape structured by joining three or more line segments at vertices.
- Angle rule for polygons: in any triangle the sum of three angles is 180 degrees. And in any quadrilateral, the sum of four angles is 360 degrees.
The sum of interior angles of n sided polygon = (n - 2) × 180 degrees.
- Types of Polygons:
- Pentagon: A five-sided figure
- Hexagon: A six-sided figure
- Heptagon: A seven-sided figure
- Octagon: An eight-sided figure (like the octopus)
- Nonagon: A nine-sided figure
- Decagon: A ten-sided figure (like decathlon)
- Regular polygons: for a polygon to be regular it must be equilateral and equiangular.
GMAT Geometry: Coordinate Geometry
Coordinate geometry in GMAT is involved with connecting graphs on the Cartesian coordinate plane.
- In a coordinate plane, any point can be expressed by a pair of numerical coordinates. These pairs of numbers display the points’ distances from the place of origin on perpendicular axes. The correspondent of any particular point is the set of numbers that identifies the location of the point, such as (3, 4) or (x, y).
- Point: while solving the GMAT quant, the students can recognize any point on the coordinate plane by its coordinates, which allocate the point’s location alongside the x- and y-axes.
- Quadrant: This can be defined by the formation by the structuring of x and y axes and forming four quadrants on the coordinate plane.
- Distance formula: imagine obtaining two points, A (x1, y1) and B (x2, y2), on a line. The formula to acquire the distance between A and B is –
- Midpoint Formula: Imagine bearing two points, A (x1, y1) and B (x2, y2), on a line. The formula to deliver the distance between A and B is –
The GMAT syllabus has been a magnanimous one and students are often witnessed fretting about the time limit and how they will be able to solve the sums quickly enough to correct. The first thing a student needs to do is prepare a journal about the strength and weaknesses after assiduously reading the syllabus of GMAT. Like we discussed here the GMAT geometry part, the student needs to pen down the sections which are their strong points and similarly the ones which they find tough. Practising is the other most vital thing to do.
*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College