We just started a chapter devoted to circles in Geometry, and I decided to show you what I’m learning.
A Chord’s endpoints lie in the circle.
A Secant goes straight through the circle.
A Tangent only touches the circle at one point.
The Point of the Tangent is where the tangent touches the circle.
Now, try to classify all of the lines in this problem:
Chords- AB, AC, AD
Point of the Tangent- E
Radii (plural of Radius)- AB, AC, AD
In Geometry, we finished chapter about Spatial Reasoning. Spatial Reasoning is all about using formulas to find the lateral area, surface area, and volume of 3-D figures. First, we had to determine what figure could be made from a net, so I made a few of those problems for you to solve:
For the top one, the answer is a cylinder, because the two circles go on top of the rectangle to make a cylinder.
For to bottom one, the answer is a pentagonal pyramid, because the triangles go up to make a pyramid over the pentagon, which is the base.
One lesson that we learned in Geometry this week is estimating the area of irregular shapes. I made a problem below:
You have to count the squares and the half-squares to make an estimate.
Did you get it yet?
The answer is 37.
For this week’s Math Blog Post, I drew a picture of how you can solve the height of a shadow. It doesn’t have to be just used for shadows, however.
Let me explain:
Step 1: Convert the feet into inches by multiplying by 12. Fred is 5 feet, 2 inches, which is 62 inches. The building is 50 feet, 2 inches, which is 602 inches. The building’s shadow is 60 feet, which is 720 inches. Remember that we are solving for Fred’s shadow.
Step 2: Put the inches into a formula:
Fred’s height Building’s height
__________ = _____________
Fred’s shadow Building’s shadow
The above formula is put into effect in the picture above. When you multiply 62 (Fred’s height) by 720 (Building’s shadow), you get 44,640.
Step 3: Divide.
Divide 44,640 by 600, and you get 74.4. But that’s not the answer. You must divide 74.4 by 12 to put it into feet and inches. 74.4 divided by 12 is 6.2, which is rounded to 6 feet, 2.5 inches.
The Triangle Inequality Theorem goes as follows:
“The sum of any two side lengths of a triangle is greater than third side length.”
This means that A and B must be greater than C. If it isn’t greater, then the triangle’s sides don’t match.
For example: A is equal to 4, B is equal to 3, and C is equal to 7.
This WOULD NOT be a complete triangle because 4+3=7.
Let’s try another one: A is equal to 34, B is equal to 21, and C is equal to 50.
This WOULD be a complete triangle because 34+21=55, and 55 is more than 50.
Got it? Good!
Today I will be explaining two geometry theroems- the Isosceles Triangle Theorm and the Equiangular Triangle Theorm.
Isosceles Triangle Theorm– This theorm states, “If two sides of a triangle are congruent, then the angles opposite it are congruent.” This theorm can be used the prove congruence in isosceles triangles.
Equiangular Triangle Theorm– This theorm says, “If a triangle is equilaterial, then it’s also equiangular.” It can be used for algebra problems within geometry.