1st Geometry Journal By Daniel Escobar

What are points, lines, and segments? Point: A dot in space that indicates something or a location.Pic:. Line: A straight conection of dots that go for ever. Pic: Segment: A piece of line that has a begining and an end.

What are rays and Planes Plane: a flat surface Pic: Rays: A conection of dots that have one begining and go on for ever How are a line, a segment, and a ray related to each other? 1. All of them make shapes.

What is the difference between a collinear and a coplanar point Collinear point: Points that lie in the same line. Collinear = line Coplanar Point: Points that lie in the same plane. Coplanar = Plane

Noncollinear vs Noncoplanar Noncollinear: points not on the same line Noncoplanar

What is an intersection? An intersection is the set of all points that two or more figures have in common. My def: when two lines cross each other. Pic:

What is the difference between a postulate and an axiom, and theorem? Postulate/axiom is a statement that is accepted as true without proof. A Theorem is a statement that you can prove. If you have proven a theorem, you can use it as a reason in later proofs.

What is a Ruler Postulate Ex.1 Ex.2 Ex.3 1 A ruler postulate tells us that the points on a line can be paired on a one-to-one with a real number

What is a Segment Addition Postulate? The Segment Addition Postulate states that if B is between A and C then AB + BC =AC Ex.1 DF + FG = DG Ex.2 GT + TE = GE abc D F G G T E

How to find the distance between two points on a coordinate plane? A coordinate Plane is a plane that is divided into four regions by a horizontal line (x-axis) and a verticle line (y-axis). The Distance between two points (x1, y1) and (x2, y2) is found with the following formula, the distance formula: d=√¯¯¯¯¯¯¯¯¯ Ex.1 d=√¯¯¯¯¯¯¯¯ = √¯¯¯29 Ex.2 d=√¯¯¯¯¯¯¯¯¯ =√¯¯¯5.4 Ex.3 d=√¯¯¯¯¯¯¯¯¯ =√¯¯¯15 (x2-x1)^2 + (y2-y1)^2 (1- -4)^2 + (-2-0)^2 (-4-1)^2 + (-4- -2)^2 (-2- -2)^2 + (-8-7)^2

Congruence vs. Equality When something is congruent, it is exactly the same/ same measure. Ex: AB ≅ CD When something is equal, it means it has the same value. Ex: 2=2 They both compare two numbers/ solutions/products. Both relate to having two same products.

What Is the Pythagorean Theorem? The Pythagorean Thereom states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. a 2 + b 2 = c = = c 2 √52= c 7.2 = c = = c 2 √50= c 7.07 = c = = c 2 √85= c 9.2 = c 9

Angles An angle are two rays that share a common endpoint. An angle is measured by 3 points. Ex: ∠ ABC. The letter in the middle is the vertex. There are 4 types of angles Right angle: Measures 90° Acute angle: Less than 90° Obtuse angle: more than 90° Straight Angle: Measures 180°

What is an Angle addition postulate? The Angle addition postulate states that if S is I the interior of ∠ PQS + m ∠ SQR = ∠ PQR. Ex.1 m= ∠ JKM if m ∠ JKL= 42° and m ∠ LKM=28°= 14° Ex.2 m ∠ DEG=37° and m ∠ DEF=84° find m ∠ GEF (84-37)= 47°= ∠ GEF Ex.3 m ∠ LKM if m ∠ JKL =56.4° and m ∠ JKM =82.5° ( ) = 26.1= m ∠ LKM

Midpoint A midpoint is a point that bisects, or divides a segment into 2 congruent segments. It can be found by dividing the measurements of the segments by two. Ex: AB=8 then AM=4, BM=4. AM=BM. CD= 5 CM=2.5, DM=2.5 AB=6 AM=3, BM=3 AC, AB =2y and BC 8y-3 2y= 8y-3 -8y -8y -6y=-3 y=2 AB=4, BC= 13, AC = 17

Angle Bisector An Angle bisector is a ray that divides an angle into 2 congruent angles. To construct one you will need a compass. And follow the instructions on the picture below.

What are adjacent, vertical and linear pairs of angles?? Adjacent angles: Two Angles that have the same vertex and share side. Linear Pairs: are two angles that create a straight line Vertical Angle: are two nonadjacent angles formed by two intersecting lines.

Complementary vs. Supplementary Complementary angles: are two angles that add up to 90° Supplementary angles: are any two angles that add up to 180° 52°38° 55° 125°

How to find perimeter and area of te following shapes. Rectangle: P=2L +2w, A =Lw Ex: L=2cm w= 5cm (P=2 +25) P=27cm, (A=2x5) A=10 cm 2 Triangle: P= a+b+c, A= 1/2bh Ex: a=8, b=(x+1), c= 4x, and h=6. P=5x +9, A= 3x+3 Square: P= 4s, A=s 2 Ex: 10 cm (P= 10x4) P=40 cm, (A=10 2 ) A=100 cm

How to find the area and circumference of a circle Area of a circle: A=(pie) 2 Ex: 4cm 4(pie) 2 =16x(pie) ≈50.24 cm 2 8cm ≈ cm 2 Circumference of a Circle: C =2(pie)r (R=radius: a segment of a circle one of its endpoints are the center of the circle and another point on the circle.) Ex: 4 cm C=8(pie) ≈25.12 C= 16(pie) ≈50.24

5 step process 1 st Read and Analyze the Question 2 nd Find important info. And rewrite it 3 rd Visualize the information you just wrote 4 th Solve the equation 5 th Write the answer

Transformations Transformation: Change of position of an object. Image A transform A A prime ∆ABC ∆A’B’C’ There are 3 types of transformations: Translation Reflection Rotation

Translation A B C A’ B’ C’ Translation slides an object in any direction.

Reflection Reflection reflects/mirrors a figure across the line If across the x axis (x,y) -> (x,-y). If across y axis (x,y) -> (-x,y) prime

Rotation Rotation is when you rotate a figure around a point. Prime

Thank you for your patience…