<body><script type="text/javascript"> function setAttributeOnload(object, attribute, val) { if(window.addEventListener) { window.addEventListener('load', function(){ object[attribute] = val; }, false); } else { window.attachEvent('onload', function(){ object[attribute] = val; }); } } </script> <div id="navbar-iframe-container"></div> <script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script> <script type="text/javascript"> gapi.load("gapi.iframes:gapi.iframes.style.bubble", function() { if (gapi.iframes && gapi.iframes.getContext) { gapi.iframes.getContext().openChild({ url: 'https://www.blogger.com/navbar.g?targetBlogID\x3d14084555\x26blogName\x3dPre-Cal+30S\x26publishMode\x3dPUBLISH_MODE_BLOGSPOT\x26navbarType\x3dBLUE\x26layoutType\x3dCLASSIC\x26searchRoot\x3dhttp://pc30s.blogspot.com/search\x26blogLocale\x3den_US\x26v\x3d2\x26homepageUrl\x3dhttp://pc30s.blogspot.com/\x26vt\x3d931551856370134750', where: document.getElementById("navbar-iframe-container"), id: "navbar-iframe" }); } }); </script>

Wednesday, November 30, 2005

My Scribe

Hello to everyone!  Today’s class started off with two investigations.  Investigation number nine and investigation number ten, which had to do with circle geometry.  

Investigation 9:

A cyclic quadrilateral is a quadrilateral all of whose vertices lie in the circumference of a circle.

First we had to construct a polygon with all four points on the circumference.  After that, for that quadrilateral we measured the sum of the opposite angles and found out that they were equal to 180°.  We then did those same steps two more times to confirm that it wasn’t just for that one type of quadrilateral.  The last step for this investigation was to articulate a general rule.  We found out that “If two angles are opposite each other in a cyclic quadrilateral, then the angles are supplementary.”

Investigation 10:

The diagonals of convex polygons are drawn at a single vertex.  Complete the table of values showing the relation between the number of sides in the polygon and the number of triangles formed.

In conclusion, a convex polygon with n sides can be divided into   n - 2    triangles.

You have learned that the sum of the interior angles of a triangle is 180°.  Complete the following table.

Refer to the preceding table.  Describe in words the relation between the number of sides in a polygon and the sum of its interior angles.

The sum of the interior angles is found by the number of sides (n) subtract two, then
Multiplied by 180°.

Again, referring to the table, write a formula that describes this relation.
The sum of the interior angles of a polygon with n sides = ( n - 2 )( 180° )

After all of that we then went into our dictionaries to take some notes.  Here they are:

Perpendicular Bisector Theorem:

Part I     If a line bisects a chord and passes through the center of a circle then it is      perpendicular to the chord.

Part II     If a line is perpendicular to a chord and passes through the center of a circle then it bisects the chord.

Inscribed-central Angle Theorem:

Part I     If a central angle and an inscribed angle are subtended by the same arc then the central angle is twice the inscribed angle.

Part II     If an inscribed angle and a central angle are subtended by the same arc then the inscribed angle is half the central angle.
A.K.A. “The star trek theorem”

Special Case:
     Inscribed-diameter (Thales) theorem
An inscribed angle subtended by a diameter is always 90°.

Inscribed Angle Theorem:

If two (or more) inscribed angles are subtended by the same arc then they are congruent.

Parallel Chord Theorem:

The arcs between parallel chords are congruent.

Congruent Chords Theorem:

Congruent chords subtend congruent arcs.

The next scribe is: (


Post a Comment

Links to this post:

Create a Link

<< Home