Geometry and Trigonometry Basics for the SAT

Welcome to SAT Geometry Essentials! Today we'll explore fundamental shapes and formulas.We'll cover four essential shapes: triangles, rectangles, circles, and polygons.Let's start with triangles. Every triangle has three angles that sum to 180 degrees.The area of a triangle is one-half times base times height.Next, let's look at rectangles. They're defined by their width and height.For rectangles, we need to know two key formulas: area equals width times height, and perimeter equals two times width plus height.For circles, everything is based on the radius.Remember these essential circle formulas: area equals pi r squared, and circumference equals two pi r.The Pythagorean theorem is crucial for right triangles.It states that a squared plus b squared equals c squared, where c is the hypotenuse.Let's solve a typical SAT problem using these formulas.To find the area of a rectangle, we multiply width times height.Plugging in our values: five times twelve.The area is sixty square units.Now that we've covered the essential shapes and formulas, we're ready to move on to trigonometric ratios.In trigonometry, we use three main ratios to find missing sides and angles in right triangles.These ratios are based on the relationship between the sides of a right triangle relative to an angle theta.The first ratio is sine, which equals opposite over hypotenuse.Next is cosine, which equals adjacent over hypotenuse.And finally, tangent equals opposite over adjacent.Now let's see how to apply these ratios to solve real-world problems.Here's a common SAT problem: Finding the height of a building using an angle of elevation.We need to find the height of a building when we know the angle of elevation is thirty-five degrees and we're standing fifty meters away.Let's solve this using our calculator. First, we'll use tangent since we're finding opposite over adjacent.After getting tangent of thirty-five degrees, multiply by the distance of fifty meters.This gives us a building height of thirty-five meters.Remember to identify the given angle and sides before choosing which trigonometric ratio to use.First, let's understand complementary angles, which sum to 90 degrees.Next are supplementary angles, which sum to 180 degrees.Vertical angles are always equal when two lines intersect.When parallel lines are cut by a transversal, several angle relationships emerge.The thirty-sixty-ninety triangle has special side ratios that are crucial to remember.Similarly, the forty-five-forty-five-ninety triangle has its own unique properties.Let's review some key SAT problem-solving strategies.And here are some time-saving tips for multiple choice questions.Let's review the key points to remember for the SAT.Good luck on your SAT!