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Geometry Puzzles and Brain Teasers

Total Number of Triangles Puzzle

How many triangles are there in the figure below?

 

Solution to this Geometry Triangle Puzzle problem is given in the video below!


 


Total Number of Rectangles Puzzle

How many rectangles are there in the figure below?

 

Solution to this Geometry Rectangle Puzzle is given in the video below!


 


Total Number of Upright SQUARES in a Square

How many upright Squares are there in the following square?

The key is to understand vertices of any given upright square and a diagonal line of the largest square to see how many translations of that given upright square you can have. As such, there is a summation-derived FORMULA you can actually use for any largest size square to find the total number of possible upright squares contained within it!

 

 

Solution to this Geometry Square Puzzle is given in the video below!


 


Total Number of Upright RECTANGLES in a Square (or Rectangle)

How many upright Rectangles are there in the following square?

The key is to understand vertices of any given upright rectangle to see how many unique translations of that rectangle are possible. As such, there is actually a summation-derived FORMULA you can utilize for the largest square or rectangle of any size to find the total number of possible upright rectangles within it!

 

Solution to this Geometry Rectangle Puzzle is given in the video below!


 


Total Number of Upright SQUARES in a Rectangle

How many upright Squares are there in the following rectangle?

The key is to understand vertices of any given upright square to see how many translations of that given square you can have. As such, there is a summation-related FORMULA you can actually derive for any size rectangle to find the total number of possible upright squares contained within it!

 

Solution to this Square Rectangle Geometry Puzzle is given in the video below!


 


Total Number of Upright & Tilted SQUARES in a Square

How many upright and tilted Squares are there in the following square?

The key is to use vertices of any given largest square to see how many translations of a given smaller square you can have. As such, there is a summation-derived FORMULA you can actually use for any size square to find the total number of possible upright and tilted squares contained within it!

 

Solution to this Square Geometry Puzzle example is given in the video below!


 


Total Number of Upright & Tilted SQUARES in a Rectangle

How many upright and tilted Squares are there in the following rectangle?

The key is to use vertices of any given rectangle to see how many translations of a given square you can have. As such, there is a summation-derived FORMULA you can actually use for any size rectangle to find the total number of possible upright and tilted squares contained within it!

 

Solution to this Rectangle Geometry Puzzle example problem is given in the video below!


 

Law of Sines problems

Law of Sines word problem example

A radio antenna is attached to the top of the building. From a point 12.5 meters from the base of the building, on level ground, the angle of elevation of the bottom of the antenna is 47.2 degrees and the angle of elevation of the top is 51.8 degrees. Find the height of the antenna.

 

Solution to this Law of Sines word practice problem is provided in the video below!



 

Law of Sines Triangle Area PROOF problem

Show that for any triangle the area is one-half the product of any two sides and sine of the angle formed between these sides. That is, 

 

Solution to this Law of Sines Triangle Area PROOF practice problem is provided in the video below!



 

Two Column Algebra Proof problems

Two Column Algebra Proof Fraction example question

Prove that if 

then

 

Solution to this Two Column Algebraic Proof practice problem is given in the video below!



Two Column Algebra Proof Division example problem

Prove that if 

then

 

Solution to this Two Column Algebraic Proof practice problem is given in the video below!



Two Column Geometry Proof problems

Two Column Geometry Proof Intersecting Lines example problem

Given: GA = RA, AH = AT

Prove: GT is congruent to RH

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Trapezoid example

Given: AD = 8, BC = 8, and BC is congruent to CD

Prove: AD is congruent to CD

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Circle example question

Given:  is a diameter

Prove: (CD)2 = (AD)(DB)

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Triangle example problem

Given:

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Triangle example #2

Given: with the bisector of

Prove: BFDE is a rhombus

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Circle example question #2

Given: Circle with center O and diameter  

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Kite example problem

Given: Kite ABCD with

E, F, G, H are midpoints of

Prove: EFGH is a rectangle

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Triangle example #3

Given: bisects

is a perpendicular bisector of

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Triangle example question #4

Given:  is isosceles and  

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Parallel Lines Transversal Triangle example problem

 

Given:

bisects  

bisects

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Theoretical & Math Proof problems (complete Playlist)

Explore a variety of Theoretical and Proof examples and practice problems applicable to Algebra, Geometry, Trigonometry, Precalculus, Calculus, and Discrete Math courses.





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