How to Study Math: Geometry

Geometry Proofs List

• Parallel Lines. If any two lines in the same plane do not intersect, then the lines are said to be parallel.
• Corresponding Angles.
• Vertical Angles.
• The Definition of Isosceles Triangle.
• Isosceles Triangle Theorem.
• Acute Triangle/ Obtuse Triangle.
• Perpendicular.
• Right Angle/ Acute Angle/ Obtuse Angle.

Use two column proofs to assert and prove the validity of a statement by writing formal arguments of mathematical statements.

Practicing these strategies will help you write geometry proofs easily in no time:

1. Make a game plan.
2. Make up numbers for segments and angles.
3. Look for congruent triangles (and keep CPCTC in mind).
4. Try to find isosceles triangles.
5. Look for parallel lines.
6. Look for radii and draw more radii.
7. Use all the givens.

Proofs are hard because you are not used to this level of rigor. It gets easier with experience. If you haven’t practiced serious problem solving much in your previous 10+ years of math class, then you’re starting in on a brand new skill which has not that much in common with what you did before.

1. Diagram for success. Geometry is the study of the relationships between points, lines, surfaces, angles, and shapes.
2. Know your properties and theorems.
3. Understand Euclid’s postulates.
4. Learn the language of math.
5. Know your angles.
6. Know your triangles.
7. Figure out what you want and what you’re given.
8. Now fill in the rest.

Equation of a Circle, Standard Form (Center anywhere) where r is the radius of the circle, and h,k are the coordinates of its center.

Practically speaking, you can just memorize that h = –b / (2a) and then plug your value for “h” back in to “y =” to calculate “k”. If you’re allowed to use this formula, you can then more quickly find the vertex, because simply calculating h = –b / (2a) and then finding k is a lot faster than completing the square.

The letter “K” in a circle is a certification mark indicating Kosher products certified by OK Laboratories, of which the administrator is Rabbi Don Yoel Levy, succeeding his father Rabbi Bernard Levy.

(h, k) is the vertex of the parabola, and x = h is the axis of symmetry. • the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0). • the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0).

Standard Form. The quadratic function f(x) = a(x – h)2 + k, a not equal to zero, is said to be in standard form. If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h,k).

The vertex form of a parabola’s equation is generally expressed as: y = a(x-h)2+k. (h,k) is the vertex as you can see in the picture below. If a is positive then the parabola opens upwards like a regular “U”.