1st Geometry Journal

1. 1st Geometry Journal By Daniel Escobar

2. What are points, lines, andsegments? • Point: A dot in spacethatindicatessomethingor a location. Pic: . • Line: A straightconectionofdotsthatgoforever. Pic: • Segment: A pieceoflinethat has a beginingandanend.

3. What are raysand Planes • Plane: a flat surfacePic: • Rays: A conectionofdotsthathaveonebeginingandgoonforever • How are a line, a segment, and a rayrelatedtoeachother? • 1. Allofthemmakeshapes.

4. Whatisthedifferencebetween a collinearand a coplanarpoint • Collinearpoint: Pointsthatlie in thesameline. Collinear= line • CoplanarPoint: Pointsthatlie in thesameplane. Coplanar = Plane

5. NoncollinearvsNoncoplanar • Noncollinear: points not on the same line • Noncoplanar

6. Whatisanintersection? • Anintersectionisthe set ofallpointsthattwoor more figures have in common. My def: whentwolines cross eachother. • Pic:

7. Whatisthedifferencebetween a postulateandanaxiom, andtheorem? • Postulate/axiomis a statementthatisaccepted as truewithoutproof. • A Theoremis a statementthatyoucanprove. • Ifyouhaveproven a theorem, you can use it as a reason in laterproofs.

8. What is a Ruler Postulate A ruler postulate tells us that the points on a line can be paired on a one-to-one with a real number • Ex.1 • Ex.2 • Ex.3 7 12 1 11 14 2 6 13 9

9. 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 a b c G D F T E G

10. 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

11. 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.

12. 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. a2 + b2 = c2 62 +42 = 52 52 = c2 √52= c 7.2 = c 92 + 22 = 85 85 = c2 √85= c 9.2 = c 52 + 52 = 50 50 = c2 √50= c 7.07 = c 9 6 5 4 2 5

13. 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°

14. 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° (82.5- 56.4) = 26.1= m∠LKM

15. 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

16. 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.

17. 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.

18. 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° 125° 55°

19. 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 cm2 • 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=s2 Ex: 10 cm (P= 10x4) P=40 cm, (A=102) A=100 cm

20. 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 cm2 8cm ≈ 67.14 cm2 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

21. 5 step process • 1st Read and Analyze the Question • 2nd Find important info. And rewrite it • 3rd Visualize the information you just wrote • 4th Solve the equation • 5th Write the answer

22. 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

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

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

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

26. Thank you for your patience…