Another from Nathan....

Given Triangle ABC where AC=BC, Angle ACB = 96 degrees, D is a point somewhere inside ABC such that Angle DAB = 18 degrees and Angle DBA = 30 degrees.  What is the measure (in degrees) of Angle ACD?

Thanks Nathan...

November Challenge

This one also comes from Nathan on the Geometry Math Team...


Prove that the LARGEST ANGLE of ANY TRIANGLE is ALWAYS GREATER THAN OR EQUAL TO 60 degrees.


I would recommend solving it by indirect proof.  Start by saying "What if the largest angle is less than 60? ...

	Chapter 4 Extra Credit Challange!

An art student wants to make a painting with a simple geometric pattern. She starts with a square. She divides this square into two congruent triangles. Then she divides each of these triangles into two smaller congruent triangles. She repeats the process seven more times. What does her pattern look like in the end?

1.  Show that the two triangles are congruent using the Hypotenuse-Leg Theorem.

2.  Use your knowledge of the Hypotenuse-Leg Theorem to divide each triangle in the figure above into two smaller congruent triangles. Repeat the process six more times.

3.  How do you know that the triangles at each step are congruent?

4.  How many triangles of the smallest size are shown?

5.  How many triangles are shown if they each contain 64 of the smallest-sized unit?

6.  How many triangles are shown if they each contain nine of the smallest-sized unit?

This one from Nathan from the Geometry Math Team.  See what you can do with it.

CHAPTER 3 Blog Spot Questions and Discussion

We have properties of Reflexive and Transitive for both Property of Equality (Using Equal sings) and Congruence (Using the Congruence symbol) but we only have Substitution Property of Equality, not Substitution Property of CONGRUENCE.  Discuss why and figure out how to circumnavigate this problem. 



How is Substitution Property of Equality different from Transitive Property of Equality?

Chapter 2 Challenge

One aspect of geometric thinking is the ability to look at a group of shapes and find some common features that define the group. For example, you know that rectangles are part of the set of figures called quadrilaterals.

 

At some point, you may be asked to classify objects based on examples and non-examples. Look at the two sets of objects below. (“Wamps” is a made-up name.)

Which of the following objects are wamps?

A.   

B. 

C. 

Notice that the wamps are all closed figures. The non-wamps are either open figures or two closed figures joined at a single point. So figures A and C above are wamps.

Look at the two sets of objects below. (“Flupes” is a made-up name.)

 

A. 

B. 

C. 

1.  Create a group of figures with certain characteristics and give them a made-up name. Then create a set of figures that are non-examples for your group. Finally, write a definition for the figures in your group.

 
  

How to Enter Your Comments for Extra Credit

1.  Click onto Comment under the section you want to comment on
2.  Log in using the same user name you use to log in onto EDMODO followed by "@hcs-students.net "
3.  Enter the same password you use for EDMODO

The extra credit challenge in class today was to see how many unique planes could be identified inside a cube.  Using the cube below: 

Identify how many planes can be made inside or on it and name all of them.   

Welcome

Welcome to the blog site for Mr. Rushano's Geometry class at Hoover High School.  It is my hope we will use this site to discuss in detail what we study in class.  It is my intention to put summaries of each unit on this blog and for you, the students, to question and comment on what we learn and discuss in class. This is your opportunity to ask detailed questions and discuss Geometry more in depth than we can in class.  I look forward to reading what you think of the subject.  I only ask that you be respectful and concentrate your comments about Geometry.  Thanks!