I have recently started doing introduction to proof for geometry, and i don understand it too well, So can someone please help me understand how to do it effectively?
Answers
Answer:
Most of us started our earliest rudimentary lessons in geometry when we stacked our first building blocks or learned to fit a triangle into a triangle-shaped hole.
By this point, you’ve learned that there’s a little more to geometry than that. That’s why we put together 11 study tips below to help you conquer geometry class. Just think of these as your building blocks for geometry success.
1. Diagram for success.
Geometry is the study of the relationships between points, lines, surfaces, angles, and shapes. So naturally, drawing diagrams is a must!
The relationships, properties, and theorems will be easier to understand when you have a diagram! And trust us, don’t rely on your mental math ability to do this.
As they say, a picture is worth a thousand words. Just be sure to pay attention to the proportion of lines and angles. Diagrams only help if they’re labeled accurately…
To start your diagram, mark down everything given to you in the problem. If you have parallel lines, mark them as such! If you have an isosceles triangle, make sure you have two equal sides! If you know lengths of edges or degrees of angles, write them down! That way when you’re thinking through your diagram, you have all the information you need.
You wouldn’t want to do a 100-piece puzzle that’s missing a few pieces. Just like you don’t want to do a geometry problem without all the given information in the diagram.
2. Know your properties and theorems.
Properties of: lines, parallelograms, and angles.
Theorems of: lines, triangles, and angles.
These are your most useful tools for drawing diagrams, forming relationships, and developing proofs! It will make your life so much easier if you’re able to recall properties and theorems for various shapes, angles, and lines.
We recommend that you make flashcards for all the properties and theorems that you need to know. Then go through them every morning and every night! That way you don’t wait until the night before the test to memorize (and understand) them.
In case you want to get a head start… here are arguably some of the most important theo rems for triangles:
Remember the word “congruent” just means that the triangles are the same size and the same shape.
Side-side-side (SSS): If two triangles have all three side measures congruent (in other words, if the three sides of one triangle are all the same length as the three sides of the other triangle), then the two triangles are congruent.
Tip: Congruent lines are often marked by short lines as in the figures below, The side with one line is congruent to the side with one line, the side with two lines is congruent to the side with two lines, etc.
Side-angle-side (SAS): If two triangles have two sides congruent and the angles in between the two sides are also congruent, then the two triangles are congruent.
Tip: Congruent angles are marked congruent by the same number of arches. In the figure below, both congruent angles have one arch.
Angle-side-angle (ASA): If two triangles have a congruent side that touches two congruent angles, then the triangles are congruent.
Hypotenuse-Leg (HL): This is a special triangle theorem that can only be used for right triangles. It states that if you have two right triangles and you know that their hypotenuses are congruent and one pair of their sides is also congruent, then the triangles are congruent.
Tip: You know you have a right triangle if there is an angle with a box in the right angle as in the figure below. Remember the hypotenuse is the side of a right triangle opposite the right angle.
Angle-angle-angle (AAA): Triangles with three equal angles are similar but not necessarily congruent.
Step-by-step explanation:
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Answer:
1• Know the postulated theorems and definition.
2• Label the drawing.
3• Know where you are going.
4•. The given is always given for a reasons !
5• If stuck ,look to introduce part of what you are proving!
Step-by-step explanation:
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