Properties of Geometric Shapes?

Test Preparation SAT Preparation
1

<p>Hi everyone! </p>

<p>My teacher gave me this to memorize for the SAT. I was wondering which properties I should memorize and if there are any additional shapes with properties that would be beneficial to memorize (if there are please post them!) Thanks and good luck to everyone tomorrow!</p>

<p>Properties of Parallelograms:
In a parallelogram:
• Opposite sides are parallel
• Opposite sides and opposite angles are congruent
• Diagonals bisect each other</p>

<p>In a rectangle:
• All the properties of a parallelogram
• Four right angles
• Congruent diagonals</p>

<p>In a Rhombus:
• All the properties of a parallelogram
• Four congruent sides
• Diagonals bisect opposite angles
• Diagonals are perpendicular</p>

<p>In a Square:
• All the properties of a parallelogram
• Four right angles
• Four congruent sides
• Congruent diagonals
• Diagonals are perpendicular
• Diagonals bisect opposite angles</p>

<p>In an Isosceles Trapezoid:
• Only one pair of opposite sides parallel
• Congruent diagonals</p>

2

<p>The last two properties under square were already listed under rhombus.</p>

<p>Perhaps you want to add the following to your list:</p>

<p>Isoscleles Triangle:
• Median, angle bisector and altitude are all the same
• Two congruent sides
• Two congruent angles</p>

<p>Equilateral Triangle:
• All the properties of an isosceles triangle
• All 3 sides congruent
• All 3 angles congruent</p>

<p>Isosceles Right Triangle:
• All the properties of an isosceles triangle
• Angles are 45,45,90
• Sides are in ratio 1:1:sqrt(2)</p>

<p>Regular Polygon
• All sides congruent
• All angles congruent
• Total interior degrees (n-2)*180</p>

3

<p>Thank you!
Can you explain what that last property of the Isosceles Right triangle means? I think your saying the two sides are a number (n) and the hypotenuse is n squareroot(2)</p>

<p>And are there any properties for circles other than the central angle= the arc and the angle that lies on the edge of the circle ( i don’t remember the name of it) is half the value of its arc.I also remember reading(but not fully understanding) about chords in the answer explanation of one of the questions in your book. Your book helped me a lot by the way so thank you for making it!</p>

4

<p>I think you understand the isosceles right triangle. This is a formula given to you right at the beginning of each math section on the SAT.</p>

<p>For circles, you should know central and inscribed angles (as you’ve said). </p>

<p>The bit about chords is the following:</p>

<p>If 2 chords in a circle have the same length, then the arcs that they intercept also have the same length (as well as degree measure).</p>

<p>Conversely, if the arcs intercepted by two chords have the same length (or measure), then the chords have the same length.</p>

<p>If I remember correctly, the problem that you’re referring to doesn’t really require this detailed information - I just included it as an afterthought for completeness.</p>

<p>A few more advanced things to know about circles:</p>

<p>If you know the radius, diameter, circumference, or area of a circle you can easily find any of the other three since each pair is related by a simple formula.</p>

<p>Given a point and a positive number r, there is exactly one circle with radius r whose center is that point (by the last fact, the same is true if we replace radius by diameter, circumference or area).</p>

<p>If you know the area of a sector with a certain angle, you can set up a ratio to get the area of the whole circle - from there you can get the radius of the circle, and from there you can get the circumference of the circle. Finally you can set up another ratio to get the arc length of the sector.</p>

<p>You can also do this procedure backwards, so that given an arc length of a sector you can find the area of the sector.</p>