Jomari's Post for May 4, 2011

Today we learned about perpendicular bisectors.
These are lines that bisect straight lines at 90°.
Here's how to make one:





We made these bisectors for several chords.

In a circle, we don't need to make crossed arcs on one side of the chord because of the center.
After wards, we answered a problem involving bisectors. It was similar to this:
A wheel is stuck in some water. The radius is 22cm and the water takes up 34cm lengthwise of the wheel. How deep is the wheel?
This is what we have to work with:

This question was difficult because of the way it was drawn, but he then realized we could do this:

WE COULD USE THE PYTHAGORAS THEOREM TO FIND B
a²+b²=c²
17²+b²=22²
289+b²=484
b²=484-289
b²=195
√ b²=√ 195²
b=13.96

22cm-13.96cm=8.04cm
THE WHEEL IS 8.04cm deep into the water

Scribepost May 3, 2011

Today in Math, we continued on circle geometry.

Basically, Backé taught us more on how to figure out the the angle of an inscribed angle by looking at its central angle. He also gave us words and diagrams that we need to know.

First, he showed us something we should know already. Here are kinds of triangles according to sides.....

Equilateral Triangles are triangles with 3 equal sides, Isosceles Triangles have 2 equal sides, while Scalene Triangles have no sides equal.

....and here are other triangles according to their angles.

Acute Triangles have 3 acute angles, Right triangles have 1 right angle and 2 acute angles, Obtuse Triangles have 1 obtuse angle and 2 acute angles.

He mentioned the word "Theta" which means an unknown angle.

Then he gave us this table....

It simply means that

• an angle that has an angle between 0 and 90 degrees is called an acute angle.
• an angle that has an angle of 90 degrees is called a right angle.
• an angle that has an angle between 90 and 180 degrees is called an obtuse angle.
• an angle that has an angle of 180 is called straight angle.
• angles that has an angle between 180 and 360 are called reflex angles.

wait there's more...


He also showed us facts about the total angle of polygons.
- sum of all angles of a triangle = 180 degrees
- sum of all angles of a quadrilateral = 360 degrees

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That is about it. Comment if I did anything wrong or if I missed stuff.

***Bring a PROTRACTOR with you because we'll be needing it in this chapter***

Hannah's post for May 2, 2011

So today we started on chapter 10, which is all about angles in a circle.

For starters, some words that we need to know are:

1. chord: a line segment with both endpoints on a circle

2. central angle: an angle formed by two radii of a circle

3. inscribed angle: an angle formed by two chords that share a common point

4. arc (of a circle): a portion of the circumference

We drew four different diagrams in class. All of which involving a circle.

They're subtended by the same arc. In other words, they share a common end point.

Homework for tonight is..

• read pg. 382 Key Ideas
• CYU #1
• Practice and apply
• Extend 18, 19, 20
• Extra Practice
• Homework book