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The GMAT geometry syllabus includes primary shapes like triangles, quadrilaterals, and straight lines. It also involves coordinate geometry like parabolas. Candidates mostly get questions on angles, side, area and perimeter of the given shape. GMAT geometry questions examine visual skills and basic measurements. So, students need to exercise strong visual skills and learn thorough geometry formulas in order to ace the GMAT Geometry section. In GMAT quant syllabus, a dominant and much more difficult genre is GMAT Geometry, apart from GMAT algebra and GMAT arithmetic.
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GMAT Geometry Topics
GMAT Geometry syllabus includes:
- Lines and angles
- Triangles
- Special right triangles
- Quadrilaterals
- Circles
- Polygons
- 3D geometry
- Rectangular solids and Cylinders
- Coordinate geometry
Geometry GMAT Concepts
Geometry concepts for GMAT include:
Lines and Angles
- A line is a one-dimensional abstraction that goes on forever.
- For any two points, there is one straight line (only one!) that passes through them.
- A line section is a segment of a straight line that has two endpoints. The midpoint is the point that divides the line segment into two equal parts.
- Two lines are parallel if they lie in the same plane and never intersect. Two lines are perpendicular if they intersect at a 90° angle.
- An angle is made when two lines intersect at a point. This point is called the vertex of the angle.
- Angles are measured in degrees (°).
- An acute angle is an angle whose degree measure is less than 90°.
- A right angle’s degree measure is exactly 90°.
- An obtuse angle’s degree measures greater than 90°.
- A straight angle’s degree measure is 180°.
- The sum of the measures of angles on a straight line is 180°.
- The sum of the measures of the angles around a point (which make a circle) is 360°.
- Two angles are supplementary if their sums make a straight angle.
- Two angles are complementary if their sums make a right angle.
- Vertical angles are opposite angles formed by two intersecting line segments.
- A line or a segment bisects an angle if it splits the angle into two, smaller equal angles.
- Vertical angles are a pair of opposite angles formed by intersecting line angles. The two angles in a pair of vertical angles have the same degree measure.
Triangles
- A triangle is a closed figure with three angles and three straight sides.
- The sum of the interior angles of a triangle is 180°.
- Each interior angle is supplementary to an adjacent exterior angle. Together, they equal 180°.
- The formula for finding the area of a triangle is ½bh.
- b = base
- h = height
- An isosceles triangle has two sides of equal length.
- An equilateral triangle has three equal sides and three angles of 60°.
- There are two kinds of special right triangles:
- Isosceles right triangles have a side relationship of 1:1:√2.
- 30°60°90° triangles have a side relationship of 1:√3:2.
- A right triangle has one 90° interior angle. The side opposite the right angle is called the hypotenuse and it’s the longest side of the triangle.
- Pythagorean Theorem for finding side lengths of a right triangle: a2+b2=c2
- Two triangles are similar if their corresponding angles have the same degree measure.
- Two triangles are congruent if corresponding angles have the same measure and corresponding sides have the same length.
Circles
- The diameter of a circle is a line segment that connects two points on the circle and passes through the center of the circle.
- The radius is a line segment from the center of the circle to any point on it.
- A circle’s central angle is formed by two radii.
- The distance around the circle is called circumference:
- C=πd
- C=2πr
- An arc is a part of the circumference of a circle.
- Length=(n/360 °)C, where n is the measurement of the central angle of the circle portion in degrees.
- The area of a circle is found with the formula A=πr2.
Polygons
- A polygon is a closed figure that has straight line segments as its sides.
- The perimeter of a polygon is the distance around the polygon (the sum of the length of all its sides).
- The sum of the four interior angles of a quadrilateral is 360°.
- Area of a square: s2
- Area of a rectangle: lw
- Area of a parallelogram: bh
- Area of a trapezoid: 1/2(a+b)h
Solids
- A cylinder is a solid whose horizontal cross section is a circle.
- Volume of a cylinder: Bh, where B is the area of the base.
- Area of the base of a cylinder: ?r2 (because, remember, a cylinder has a circular cross section)
- A cube is a rectangular solid where all the faces are squares.
- Volume of a cube: Bh, where B is the area of the base.
- A rectangular solid is a solid with six rectangular faces.
- Volume of a rectangular solid: lwh
Coordinate Geometry
- GMAT Coordinate Geometry is the largest part of the field needed in GMAT.
- The slope of a line tells you how steeply that line goes up or down the coordinate plane.
- slope = rise/run
- slope=change in y/change in x$
- The rise is the difference between the y-coordinate values of two points on the line; the run is the difference between the x-coordinate values of two points on the line.
- You can also find the slope of a line using the slope-intercept equation, which is y=mx+b, where the slope is m and b is the value of the y-intercept.
- Perpendicular lines have slopes that are negative reciprocals of one another.
- To determine the distance between any two points on a coordinate plane, you can use the Pythagorean theorem.
GMAT Geometry Tricks and Tips
Geometry in GMAT itself is one of the most difficult parts of GMAT. Within the quant section, geometry questions appear more challenging to the test-takers because the diagrams or word problems contain complex information and a range of data. With proper practice of GMAT quant, the candidates can get an idea of the types of geometry questions a little bit. Here are some tips for the candidates to ace the GMAT geometry problems:
Practice Daily
Candidates often tend to skip the practice of GMAT geometry as they focus more on data sufficiency and other algebra and arithmetic questions. However, it is not the right way to crack GMAT at all.
Regular Geometry practice is essential for solving the questions. Also, having an idea of the questions is essential. For this purpose, checking the GMAT practice papers is essential.
Memorize the Rules
It is not that easy to memorize the properties and rules of geometry at once. This too can be achieved with daily practice. We suggest the candidates maintain a copy to note the basic rules and GMAT geometry formulas.
Redraw the Structure
Sometimes, redrawing the diagram can help the candidates to solve problems accurately and quickly. Yes, this technique is considered to be a more time-consuming one, but some problems can be solved pretty easily with this.
Use the Scratch Paper Wisely
Do not forget to mark up the diagrams after redrawing it. Make sure to do this correctly because the entire calculation process is dependent on it.
Check the Time
GMAT geometry questions are pretty time-consuming and these questions often take more than 2 minutes to solve. This is up to the candidates whether they can utilize that much time in it or not.
GMAT Geometry Questions PDF
GMAT Geometry pdf is given below to give you an idea about GMAT geometry questions:
*The article might have information for the previous academic years, which will be updated soon subject to the notification issued by the University/College.
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