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Friday, December 02, 2005

Straight From The Pen of a Scribe....

Well it's my turn for scribe again. Well I guess I should start with the beginning of class, which was a surprise quiz!!! How exciting! So here is the questions on the quiz and how they are to be figured out correctly, with a few helpful hints.
The first question:

In this question you obviously had to solve for x and y and use statement and reason to explain what you did.

Well first you should have been able to figure out that angle DEF= 70 degrees(red) because it is the exterior angle to triangle ADE (blue).

The two black dots indicate that those two angles are congruent. Creating a total angle that equals 140 degrees (yellow). Using that information you then can find the value of X. X=100 degrees because angle CEF is exterior to triangle ACE.

From this information we can derive that Y= 60 degrees because angle ACE (red) is exterior to triangle ABC (blue).

And that is pretty much question one for you. Question two was were you had to find two congruent triangles and then prove it using statement and reason. For this question, instead of demonstrating the diagram I will show you how to do the proper Statement and Reason set up. For this specific question there were two different ways of accomplishing the correct answer.The first is in blue and the second is in red.

The first way is: Statement Reason
angle AFD is congruent to Opposite angles
angle EFB.
angle FAD si congruent to Given
angle FEB
Line AD is congruent to Given
line EB
Triangle FAD is congruent to
triangleFEB AAS

The second way is this: Any of this look familiar. *Looks at previous post*
Line AC is congruent to
line EC Given
Angle ACB is congruent to
angle ECB Reflexive property
Line CB is congruent to line CD Given
Triangle ABC is congruent to
triangle EDC SAS

The third and last question goes like so:

For this question we were given that the diameter is 20 cm and that the chord AB is 12 cm. We were then asked to figure out the distant between the chord and the centre of the circle. Knowing that the diameter bisects the chord we know that each half of the chord is 6 cm. We also know that the radius is 10 cm. You then construct a radi to one of the chords points creating a right triangle. You are now given two of the sides and use the pythagorean to figure the third side out which comes to 8 cm.
*Don't forget that the hypotenuse is always C. Many people forget that small point and just add the two sides given (don't worry I did it myself today). Also don't forget to include the units.*

Last but not least we put more work into our dictionaries! YAY!!!! *Always read before bed*
Congruent Chord Theorem
Congruent Chords subtend congruent arcs. Congruent chords are equidistant from the centre of a circle.
The Tangent Theorem
Two tangents drawn from a common point, exterior to a circle, are congruent.
Tangent-Radius Theorem
A tangent and radius intersect at a right angle.
Tangent Chord Theorem
The angle between a tangent and a chord is congruent to the inscribed angle subtended by the opposite side of the chord.
Cyclic Quadrilaterals
A cyclic quadrilateral, all of whose verticies lie on the circumference of a circle. Opposite angles in a cyclic quadrilateral are supplementary. a+c=180 b+d=180
Interior Angle Sum of in Any Polygon
The sum of the interior angles in any polygon given by S=180(n-2)
S is the sum of all the interior angles.
n is the number of sides in the polygon.
Example: What is the sum of the interior angles in a 12 sided polygon?
Alright that is really it guys. And the next scribe is......


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