Pablo Canga Journal 1Geometry

9-3 M2

1) Point is a mark that sets a location in space. <it can be represented by a point or circle. <can be labeled with a letter. example:

A line is a group of dots being connected in a straight line. It can go forever.

example: <-----A-------B----->

A plane is a straight and firm surface that can extend forever.

P

.P

2) Collinear Points: They are points that occur to be in the same exact line.

<---a----b---->

Coplanar points: They the points that are in the same plane. When they are not coplanar or collinear is because the points indicated or shown are not on the same line or plane as the others do.

A

B

3) Lines, segments and rays have much to do with each other because that all involve in points getting connected. a line is dots that form and go forever. a segment is a piece of a line that stops at both ends and a ray is a line that in one end it starts and then goes forever.

AB

ABAB

4) An intersection is 2 or more than 2 lines that intersect with one an other. For example you can see an X type illustration showing that line AB crosses with line BC. They are also in the same plane and when they intersect they form angles.

5) The Postulate is a true statement that can be proven as true without any proof. An axiom is kind of like that but instead this one is not necessary true. Theorem is a statement proven by postulates or another theorem.

The difference in this ones is that some are already proven as true and others not necessarily.

6) A ruler postulate is the measure of a line and it also tells us that every point can be a number. It also has to do between the distance from point to point in a line.

<---a--b-c-----d--e--f---->

every dash represents 3 inches.ac is 9 inchesbf is 30 inchesce is 21 inches

7) Segment addition postulate. As I said above this means or describes the distance or measure from point to point in a line in the same plain.

I think that at least almost everyone has used this example but it is a great example.

oA----------------------oB--------------oC

oB is between A and C then that means that the measure of distance AB plus BC equal AC.

A 4 B 4 C

AC =4

X 2 Y 5 Z

XZ =7

D 7 E 13 F DF =20

Congruency and equality have about the same idea. They both mean equality in away. Congruency means that there are 2 shapes that are exactly the same. Equality is the solution to a equation or product. The symbol used for equality is a normal equal sign. For congruency you have to use a equal sign with a little mark on the top. Both are comparing 2 things with others.

X+3=9X=6

THIS SHOWS EQUAL

THIS SHOWS COUNGRENT

Angles are two rays that share and have the same endpoint. There are 3 different types of angles and they depend of the degree they have. The angles are right, acute, and obtuse.

Obtuse is 90 or more until 180

Right angles are 90 degrees

Acute is 90 degrees or

bellow

Straight angle

Angle addition postulate is that 2 of the small angles form a big angle. For example to form a 180 you need 2, 90 degrees to form it. In other words it is 2 little angles forming a big angle. For example to make a 90 d. angle you would need a 77 and a 13 angle degrees. b) to form a 180 you would need a 60 and a 120 angles to make it. For a 125 angle you need a 25 and a 100 angle to make it.

Complementary and suplementary angles are pretty

common. Complementary angles are the ones that 2 angles form a 90 degree angle. Suplementary forms a 180 degree angle. They

can be adjacent.

Angle contruction bisector is the exact midpoint of an angle. To find it you need a compass and you have to fisrt know how to sketch and draw. This is a more precise technique than those two but this one takes longer to do but you have a much better result. This will kind of cut or separate your angle in half in 2 equal parts. You should do this steps.

Adjacent: 2 smaller angles that together form a bigger angle.Linear Pairs: two adjacent angles that form a supplementary angle that look as a line. Linear pair.Vertical: they are not adjacent angles. This happens when there is intersection.

Adjacent / linear pair /vertical

Square: If you want to get the perimeter you have to add all 4 sides together. For area square a side and there you have it.Rectangle: To get the Perimeter just add all sides. Area just x length times width.Triangle: To find perimeter a+b+c and for area the formula is bh/2.

2in

2in

Area( sqr) and perimeter equal 4inches.

6m

3m

P= 18m and area = 18m sqr

ft5

1cm 1cm

1cm

1cm

P=2cm a=2 cm square8ftA=40 ft squareP= 26 ft

ab

c A+b+c

11

1

Midpoint is the middle point of a line, segment, angle or anything. To find out here the specific midpoint is, to construct a midpoint first step is to draw a segment or line, then draw a line in the middle, then make 2 semi arcs from the endpoint to the middle. Finally make a line crossings your arcs. There is the midpoint.

Circumference is the distance around the circle. C=(pie)d for diameter C=2(pie)r. radius C=2(p)4

11.14

4m

7mm

C=2(p)743.96mm

A=(pie)r2A=3.14 times 4A=12.56

1cm2in

A=8.28cm

A Transformation when the shape or thing changes of position either by translation, rotation or reflection.

Translation: When the shape slides to any other direction. XY then changes by the sum of a and b (X+a,Y+b)

Rotation: When you rotate the shape in the same point without moving from the point.

Reflection: When your shape is in the other side of the graph but exactly in the other side. Idea of a mirror.

TRANSFORMATIONS

Pythagorean theorem is used for the right triangle.

Theory that everywhere you have this formula a₂+b₂=c₂ it will always be true no matter what.

I didn’t understand this one so I didn’t really have any examples to help teach my classmates this lesson.

If you want to get the distance of two points, you have to square X1 X2 Y1 Y2 coordinates, add them and finally square what you got. Distance=√(X1-X2)2+(Y1 -Y2)2 this is the formula you should use to solve them.

1.READ IT CAREFULLY2.WRITE DOWN INFORMATION3.DRAW A PICTURE4.WRITE AND SOLVE EQUATION5.ANSWER

5 steps to solve method

Distance of 2 points in a coordinate plane

THE EEEEENNNNDDD