Category Archives: Geometry

Kinds Of Triangles

Welcome!  If this is your first visit to my website, look around and see what’s here.   I hope it will meet your needs.  Come back often!

In addition to math help previously available here, this year you will find Algebra videos and Geometry videos.   Go ahead.  Watch the Preview here!  If you’d like to have the full video for reference, just download it at Mindbites.com.  You can save it to your computer and access it whenever you need to.  For those of my friends who are totally disinterested in math, you can watch it at 2:00 AM and it is guaranteed to cure your insomnia!

Today’s video is entitled Kinds Of Triangles.  It’s a 12-minute video that shows each type of triangle used in Geometry and takes a look at their angles and sides.  

Triangles are one of the most familar shapes in the world. As simple as a triangle is, there are several different kinds of triangles and they have different properties. We will also look at the interior, the exterior, as well as the triangle itself.

In this video you will learn all about each type of triangle. You will learn about their angles and their sides and the relationships between sides and angles. Make sure you commit all definitions to memory so when you need to write a proof involving a triangle, you will have the tools you need.

Enjoy this lesson. It’s very straightforward and not difficult at all. Just get all the details and terminology! Success is in the details!

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How Many Lines of Symmetry? (LOS)

1. Circle has infinite # LOS.
2. Parallelogram has NO LOS.
3. Rhombus has 2 LOS.
4. Reg Hexagon has 6 LOS.
5. Square has 4 LOS.
6. Rectangle has 2 LOS.
7. Reg Pentagon has 5 LOS.
8. Equilateral Triangle has 3 LOS.
9. Kite has 1 LOS.
10. Isosceles Trapezoid has 1 LOS. Non-Isosceles Trap has NO LOS.

Every regular polygon has the same number of LOS as it does sides!

Exterior Angles Of A Triangle

What do you know about the exterior angles of a triangle?

1. Each exterior angle forms a linear pair with its adjacent interior angle.
2. In other words, each exterior angle + adjacent interior angle = 180 degrees
3. Exterior angle = Sum of the two remote interior angles.
4. In other words, an exterior angle = sum of the non-adjacent interior angles.
5. In any regular convex polygon, exterior angles always add to 360 degrees.
6. In any regular convex polygon, each exterior angle = 360/number of sides.
7. You can extend a side of a polygon to form an exterior angle.
8. What else?

30-60-90/45-45-90 Triangle Relationships

30-60-90 Triangles

The side opposite the 30 degree angle is the short side. Let’s start there. This side is half of the hypotenuse…or you could say the hypotenuse is two times the short side. The hypotenuse is the longest side. That leaves the side opposite the 60 degree angle….the middle side. It is always √3 times the short side. In other words:

Short Side = x
Medium Side = √3 x
Long Side = 2x
_____________________________________________________________________
45-45-90 Triangles

The two sides opposite the 45 degree angles are congruent. The third side is √2 times the shorter sides.

Both Congruent Sides = x
Hypotenuse = x √2

Remember Your Right Triangle Trig Ratios?

SOHCAHTOA

Sin A = Opposite/Hypotenuse

Cos A = Adjacent /Hypotenuse

Tan A = Opposite/Adjacent

Remember you can use these ratios if you have a right triangle. Angle A refers to either of the two acute angles in the triangle but not the right angle. If you do not have enough info to use the Pythagorean Theorem, try using these trig ratios to solve the triangle.

What Are Skew Lines? Aren’t You Dying To Know?

Everybody needs to understand skew lines 🙂 …..before they take any end of course test.
Skew lines are lines that do not lie in the same plane. That is, they are noncoplanar. Think of two lines that are not parallel, yet they do not intersect. Those lines are skew lines.

The lines in this drawing are skew lines. They are not in the same plane. The do not intersect. They are not parallel.

Deductive or Inductive?

Way back in the beginning of the year you learned about 2 kinds of reasoning. Later you learned to write proofs. Remember how much fun that was!!!!

Inductive Reasoning: This kind of reasoning is based on patterns that you observe. Here’s an ex.
1+3=4
1+3+5=9
1+3+5+7=16
1+3+5+7+9=25
Based on this pattern, what is the sum of the first 9 consecutive positive odd numbers?
a. 49
b. 64
c. 81
d. 100

Answer: c Do you see the pattern?.

Deductive Reasoning: This kind of reasoning is based on facts…theorems, postulates, properties. When you write a proof using theorems, you are using deductive reasoning.