DesmoGirl

The hardest part of this project was moving around the diagonal lines, and also making them fit to the other lines and be equal .The easiest part of this project was making straight lines and moving them up and down or side to side ,because personally that's the easiest thing to do on a desmo calculator. The most fun part of the project for me was seeing the final product and what you have made. Because you have worked hard to make it so once your done and see how cool it looks you feel proud .

The hard part of this project for me was moving the lines to where they have to go ,and making them equal so the desmo girl looked right. The easy part of this project was making straight lines ,because personally that's the easiest thing to do on a this graph. The most fun part about this project is seeing your finished product. This is my favorite part to because you have worked so hard to see something good

Study Guide 7.4-7.6

7.4 Showing Triangles Are Similar : SSS and SAS

Side-Side-Side Similarity Theorem

-If the corresponding sides of two triangles are proportional ,then the triangles are similar .

Side -Angle -Side Similarity Theorem

-If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides that include these angle are proportional ,then the triangles are similar .

7.5   Proportions and Similar Triangles

Triangle Proportionality Theorem
-If a line parallel to one side of a triangle intersects the other the sides ,then it divides the two sides proportionally .

 

Converse of the Triangle Proportionality Theorem

       -If a line divides two sides of a triangle proportionally ,then it is parallel to the third side .

The Midsegment Theorem
       - The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long .

 
 

 

 

 

 

 

7.6   Dilation
A dilation is a transformation with center C and scale factor K that maps each point P to and image p' so P' lies on segment CP and CP' = K x CP .

O= center of Dilation
A= point
A'= image

Types of Dilation
      -If the image is smaller than the original figure ,then the dilation is a REDUCTION .If the image is larger than the dilation it is an ENLARGMENT .

Scale Factor -The scale factor of a dilation is the ratio of CP' to CP.

 

 

Study Guide 7.1-7.3

7.1   Ratio and Proportion

-A ratio is a comparison of a number a and a nonzero number b using division .
              -Ratios can be written in 3 way . (a to b ... a/b ... a:b)
-A proportion is an equation that states that two ratios are equal.
             

The numbers b and c are the means , and the numbers a and d are the extremes of the proportion .

Cross Product Property - In a proportion ,the product or the extremes is equal to the product of the means .  (a x d =c x d)

7.2    Similar Polygons

In geometry ,two figures that have the same shape are called similar .

Two polygons are SIMILAR POLYGONS if the corresponding angles are congruent and corresponding side lengths are proportional .

 If two polygons are similar ,then the ratio of the lengths of two corresponding sides is called the SCALE FACTOR.

Perimeters of Similar Polygons
     - If two polygons are similar ,then the ratio of their perimeters is equal to the ratio of their corresponding side lengths .

7.3 Showing Triangles Are Similar : AA

Angle -Angle Similarity Postulate (AA)
- If two angles of one triangle are congruent to two angles of another triangle ,then the two triangles are similar .

Project 3

A polyhedron is a slid 3 dimensional object with flat faces, straight edges ,and sharp corners or vertices .

 

 

-The polyhedron my group made was an Octahedron.

 

-A octahedron is a 3 dimensional object composed of eight equilateral triangles, four of which meet at each vertex.

 

-Or polyhedron has 6 vertices .

-In our polyhedron ornament we used the colors green and blue.

 

-The polygons used in or project where triangles and square .

 

Reflection



 

 
 
 
In this project my group made an octahedron which is a type of polyhedron. During this project I worked with Temmy, Kaitlyn ,and Laren . During class we spent around an hour working on the project and home I spent about an hour and  minutes .During this project I learned what a octahedron and what a polyhedron was. The most challenging thing about this project was putting together the pieces to make the octahedron  . Also reaching about polyhedrons and octahedrons was a little challenging .I enjoyed making the ornament and working with my group members . If I could change anything about the project it would be the materials , it might have been better with more materials.



 

Theorems Of Perpendicular Lines

Theorem 3.4: If two sides of adjacent acute angles are perpendicular, then the angles are complementary.

Theorem 3.3: If two lines intersect to form adjacent congruent angles ,then the lines are perpendicular.

Theorem 3.2: If two lines are perpendicular, then they intersect to form 4 right angles.

Theorem 3.1: All right angles are congruent. 

Perpendicual , Parallel , and Skew Lines

Today I learned about parallel ,perpendicular and skew lines. I learned that lines that parallel lines are lines that lie in the same plane and do not intersect. Perpendicular lines are lines that intersect to form an right angle. Skew lines are lines that do not lie in the same plane and don't intersect . Parallel lines and skew lines are similar because they both don't intersect, but the difference is parallel lines lie in the same plane while skew lines don't. Also skew lines and parallel lines are different from perpendicular lines because they don't intersect ,while perpendicular lines are.