Ask questions in class. Your teacher is there to make sure you have a solid grasp on the material. If you have a question, don’t hesitate to ask it. Some of the other students in the class likely have the same question. Prepare for class by reading the lesson you are going to cover ahead of time and know the formulas, theorems, and postulates by heart. Pay attention to your teacher while you are in class. You can talk to your classmates at break or after school.
Understanding the properties of shapes and visualizing them is essential to succeeding in geometry. Practice recognizing shapes in various orientations and based on their geometric properties (the measure of angles, number of parallel and perpendicular lines, etc. ).
One of your study mates may understand something that you don’t and help you out with it. You might also be able to help them understand something and learn it better by teaching them.
Align the center hole of the protractor over the vertex (center point) of the angle. Rotate the protractor until the baseline is on top of one leg of the angle. Extend the angle up to the arc of the protractor and record the degree it falls upon. This is the measurement of the angle.
If you come across a topic in your homework that you are struggling with, focus on that topic until you understand it. Ask you classmates or your teacher to help you out.
Try teaching your sibling or parent some geometry. Take the lead in a study group to explain something you know really well.
Make sure to do as many practice problems as you can from other sources. Similar problems may be worded in a different way that might make more sense to you. The more problems you solve, the easier it will be to solve them in the future.
Ask your teacher if there are tutors available through the school. Attend any extra tutoring sessions held by your teacher and ask your questions.
1: A straight line segment can be drawn joining any two points. 2: Any straight line segment can be continued in either direction indefinitely in a straight line. 3. A circle can be drawn around any line segment with one end of the line segment serving as the center point and the length of the line segment serving as the radius of the circle. 4. All right angles are congruent (equal). 5. Given a single line and a single point, only one line can be drawn directly through the point that will be parallel to the first line.
A small triangle refers to the properties of a triangle. A small angle shape refers to the properties of an angle. Letters with a line over them refer to the properties of a line segment. Letters with a line over them with arrows at each end refer to the properties of a line. One horizontal line with a vertical line in the middle means that two lines are perpendicular to each other. Two vertical lines mean two lines are parallel to each other. An equal sign with a squiggly line on top means that two shapes are congruent. A squiggly line means that two shapes are similar. Three dots forming a triangle means “therefore”.
When two lines are parallel they never intersect with each other. Perpendicular lines are two lines that form a 90° angle. Intersecting lines are two lines that cross each other. Intersecting lines can be perpendicular, but can never be parallel.
A 90° angle is also a perpendicular angle: the lines make a perfect corner.
For example: Find the length of the hypotenuse of a right triangle with side a = 2 and b =3. a2 + b2 = c2 22 + 32 = c2 4 + 9 = c2 13 = c2 c = √13 c = 3. 6
Remember, that an equilateral triangle is technically also an isosceles triangle, because it does have two congruent sides. All equilateral triangles are isosceles, but not all isosceles triangles are equilateral. Triangles can also be classified by their angles: acute, right, and obtuse. Acute triangles have angles that are all less than 90°; right triangles have one 90° angle; obtuse triangles have one angle that is greater than 90°.
Corresponding angles are identical angles in two shapes. In a right triangle, the 90-degree angles in both triangles are corresponding. The shapes do not have to be the same size for their angles to be corresponding.
Vertical angles are the two angles formed by two intersecting lines that are directly opposite each other. [16] X Research source Alternate interior angles are formed when two lines intersect a third line. They are on opposite sides of the line they both intersect, but on the inside of each individual line. [17] X Research source Alternate exterior angles are also formed when two lines intersect a third line; they are on opposite sides of the line they both intersect, but on the outside of each individual line. [18] X Research source
For example: Find the sine, cosine, and tangent of the 39° angle of a right triangle with side AB = 3, BC = 5 and AC = 4. sin(39°) = opposite/hypotenuse = 3/5 = 0. 6 cos(39°) = adjacent/hypotenuse = 4/5 = 0. 8 tan(39°) = opposite/adjacent = 3/4 = 0. 75
Make sure to label everything very clearly based on the information provided. The clearer your diagram, the easier it will be to think through the proof.
Write down the relationships between various lines and angles that you can conclude based on your diagram and assumptions. Write down the givens in the problem. In any geometric proof, there is some information that is given by the problem. Writing them down first can help you think through the process needed for the proof.
How does the problem come to that conclusion? Are there a few obvious steps that must be proved to make this work?
CPCTC: corresponding parts of the congruent triangle are congruent SSS: side-side-side: if three sides of one triangle are congruent to three sides of a second triangle, then the triangles are congruent SAS: side-angle-side: if two triangles have a congruent side-angle-side, then the two triangles are congruent ASA: angle-side-angle: if two triangles have a congruent angle-side-angle, then the two triangles are congruent AAA: angle-angle-angle: triangles with congruent angles are similar, but not necessarily congruent
The more proofs you do, the easier it will be to order the steps properly.
