how do we define circles?

How Do We Define Circles?

Circle

A circle is the set of all points in a plane at given distance froma given point.

http://www.math.com/school/subject3/lessons/S3U1L6GL.html

-Given distance is the radius

- point is called the center

Chord

A line segment that connects two points on a circle 

http://en.wikibooks.org/wiki/Geometry/Chapter_7

Diameter

A line segment through the center with endpoints on the circle

http://openhighschoolcourses.org/mod/book/view.php?id=258&chapterid=500

Tangent

A line that touches a circle in exactly one point.

http://www.icoachmath.com/math_dictionary/Common_External_Tangent.html

-Congruent circles have the same radius

-Concentric circles have the same center

Semicircle

half a circle= 180 degrees

Minor Arch- less than 180 degrees

Major Arch- more than 180 degrees

what are the special parallelograms?

What Are The Special Parallelograms?

Rhombus

A parallelogram with four congruent sides.

http://math.tutorvista.com/geometry/quadrilaterals.html



In the example above, the diagonals bisect the angles and they also bisect each other.



Rectangle

Parallelogram with four congruent angles or an "equiangular parallelogram."

http://www.geom.uiuc.edu/~dwiggins/conj28.html

The diagonals of a rectangle are congruent and they bisect each other.

Equilateral Rectangle

Equiangular rhombus

http://quizlet.com/6547298/geometry-terms-cfh-flash-cards/

Diagonals are congruent, perpendicular and they bisect each other.







how do we use the properties of trapezoids?

 

How Do We Use the Properites Of Trapezoids?

 

 

 

Trapezoids

exactly on pair parrallel sides

http://www.kidsmathgamesonline.com/pictures/shapes/trapezoid.html

 



Trapezoid Consecutive Angles Conjecture

the consecutive angles between the bases of a trapezoid are parrallel and have 180 degree supplementary angles

 

 

http://standards.ospi.k12.wa.us/FullGlossary.aspx?subject=7,PE

Isosceles Trapezoid Conjecture

the base angles of an isosceles trapezoid are congruent

 



http://www.geom.uiuc.edu/~dwiggins/conj19.html



what are the properties of kites?

 

 

What Are the Properties Of Kites?

 

 

 

Kite

two pairs of consecutive congruent sides

ex:

http://www.wyzant.com/Help/Math/Geometry/Areas/Rhombuses_and_Kites.aspx

In kite abcd, segment ab is congruent to bc because the angles are adjacent to each other. It's the same with segments ac and dc.

 

 

Properties of Kites

1) the nonvertex angles are congruent

2) diagonals are perpendicualar

3) the vertex diagnal bisects the other diagonal

4) the vertex diagonsl is an angle bisector of the vertex.

 

 

 

 

 

http://emathlab.com/Geometry/Quadrilaterals/TrapezoidsKites.php



how do we use the triangle inequality theorem?

 

 

How Do We USe the Triangle Inequality Thereom?

 

 

Triangle Inequality Theroem

 

The sum of any two sides of a triangle must greater thn the meausre of the third.

 

 

Examples:

 

 

 

http://www.mathwarehouse.com/geometry/triangles/triangle-inequality-theorem-rule-explained.php

 

 

In the example above, it shows that any two sides must be greater than the third side to create a triangle.

 

 

 

 

http://www.onlinemathlearning.com/triangle-inequality.html

 

 

This is another example to show how triangle inequality theroem works. If you add 4+7, it would equal 11, which is greater than 8. If you add 7+8, it would equal 15, which is bigger than 4. Also if you add 4+8, it would equal 12, which is still greater than 7.

 

In order for the theorem to work, any two sides must be greater than the third side, other wise it won't be considered a triangle.

 



how can we prove that triangles are congruent?

How Can We Prove that Triangles Are Congruent?

Two triangles are congruent if and only if all their corresponding sides and angles are congruent.

http://library.thinkquest.org/20991/geo/ctri.html

In the example, triangle ABC and triangle XYZ are both congruent. You can tell becasue line AB and line XY have the same side measure of 10 units. Also, both triangles have the same angle measures in the same parts of the triangle. The sum of 65 and 75 is 140. To find the missing angle, you take the sum os the two existing measures and subtract it from 180. You'd get 40, and to check it  you'd add all the numbers to get 180.

The triangles are congruent because they both have the same measurments of all sides and angles.





how do we use the triangle sum conjecture?

 

How Do We Use the Triangle Sum Conjecture?

 

 

 

A conjecture is the sum of measures of the angles in every triangle is 180 degrees. Using the conjecture involves using alternate interior angles to determine the other angles meausres.

 

 

Examples:

 



 

http://www.geom.uiuc.edu/~dwiggins/conj04.html

 

In the example, angles A,B, and C in triangle ABC all equal to 180 degrees. The angle measures can also be determined by alternate interior angles:

 

 

 

 

http://bbs.sachina.pku.edu.cn/stat/math_world/math/t/t285.htm

 

 

 

This example shows a triangle abc underneath line segment DE. A is the midpoint of line DE. The alternate interior angles are a and b because they're not only supplementary to the line segment, but aslo a linear pair of angles.