Download to read offline
Uploaded byBan Lara
Journal 1
- A point is a dot that describes a position, a line extends infinitely in one direction connecting points, and a plane extends infinitely in two directions forming a flat surface. - Collinear points lie on the same line while coplanar points lie on the same plane. An intersection occurs when lines, rays, or segments cross. - A postulate is a statement accepted as true without proof, a theorem is a proven statement, and transformations include translations, rotations, and reflections. - The Pythagorean theorem relates the sides of a right triangle, and finding the midpoint, area, and perimeter of shapes like circles, triangles, rectangles involves specific formulas.
Journal 1
- 1.
- 2. A point isa dot that describes the position of something somewhere.A line is a straight connection of points that extends forever.A plane is a flat surface that goes on forever on all directions.Points, Lines and Planes
- 3.
- 4. Collinear: Points thatare on the same line are collinear.Coplanar: Points that are on the same plane.The similarities that they have are that they both have points that are on the same surface. A difference is that collinear have to be on the same line but coplanar don’t have to be aligned just on the same plane.Collinear and Coplanar
- 5.
- 6. Line: A straightconnection of points that extends forever.Segment: A piece of a line with a beginning and end.Ray: A line that goes on one direction only.They are related because they all connect points that are collinear.Line, Segment and Ray
- 7.
- 8. An intersection iswhen two lines, rays or segments cross each other.Examples: Intersection
- 9. Postulate/Axiom: A postulateor axiom are the same thing just with different names. A postulate is a statement that is accepted as true without proof.Theorem: A theorem is a statement that has been proven by previous postulates or another theorem.The difference is that a theorem has already been proved and an axiom or postulate doesn’t necessarily have to be proven.Postulate, Axiom and Theorem
- 10.
- 11. The ruler postulatetells us the distance of a line. It tells us that every point in a line can be described by a real number. The two points are described as AB and the distance between them can be found by the subtraction of lA-Bl.Ruler Postulate
- 12.
- 13. It’s used tofind the distance between two points in a line. In other words you find the measure of a segment. The postulate is described by AB+BC=AC. Meaning the distance from point A to the midpoint and the midpoint to point C will give you the overall distance of the segment.Segment Addition Postulate
- 14.
- 15. The distance betweentwo points can be found by inserting the correct numbers on the distance formula.d=Distance Formula (finding the distance between two points)
- 16.
- 17. Congruence is measurementsthat might not know the value.Equality is the same measurement and must know the value.The shape is congruent if it has the same shape of another and same size and can be transformed in any way that doesn’t alter it’s shape but it’s equal if it’s exactly the same shape and size. Congruence and Equality
- 18.
- 19. The sum ofthe areas of two squares on the sides A and B equals the area of the square C (hypotenuse). The formula is:Pythagorean Theorem
- 20.
- 21. An angle isa formation of two rays that share a vertex (endpoint). Angles can be measured with a protractor.The angle includes a vertex and at least two rays that have to form at least one corner.Angles
- 22. Acute:Is the typeof angle that has a measurement smaller than 90 degrees.Right:Is the angle that has a measurement of exactly 90 degrees.Obtuse:Is the type of angle that has more than 90 degrees.Types of Angles
- 23. Straight:Is an angle that has a measure of 180 degrees.Complementary:Is when two angles share a vertex and a side. Their measure-ments add to 90 degrees.Supplementary:Is when two angles share a vertex and side but add up to 180 degrees.More types of Angles
- 24. It states thatif you add one adjacent angle to the other, it will give you the measurement of the whole angle. For example: If a point S lies in the interior of ∠PQR, then ∠PQS + ∠SQR = ∠PQR.Angle Addition Postulate
- 25. Examples:According to angleaddition postulate, m∠DAC + m∠CAB = m∠DAB. So, m∠DAB = 35° + 30° = 65°
- 26. The midpoint isa point in exactly the middle of a segment. It can be constructed by using a compass and marking to x’s on the top and on the bottom. To do this you need to set the compass to a little more than half the segment and use the same measurement on one side and on the other. You can also find it by using the formula: where P1(X1,Y1) and P2(X2,Y2) are inserted.Midpoint
- 27. Examples:Find the midpointbetween (–1, 2) and (3, –6). Find the midpoint between (6.4, 3) and (–10.7, 4).
- 28. To bisect anangle you need to create a line with your compass on both rays. From that point where the ray intersects the compass-line you draw another line in front of the vertex, with the same measurement as before.Example:Angle Bisecting
- 29. Adjacent:Are two anglesthat share a vertex and a side.Linear Pairs:Are two angles that form a straight line.Vertical Angles:Are angles that are non adjacent when two lines intersect, they’re congruent.Adjacent, Linear Pairs and Vertical Angles
- 30. These angles arecommon because they both are angles that share a vertex and a line, the difference is that complementary angles add up to 90 degrees and supplementary add up to 180 degrees.Examples:Complementary SupplementaryComplementary and Supplementary angles
- 31. Square:To find theperimeter you multiply by four the side and to find the area you square the length.P=s+s+s+s orP=4*sA=s^2Rectangle:The perimeter is the sum of the length multiplied by two and width multiplied by two. The area is length times width.P=2L+2WA=l*wTriangle:To find the perimeter you add the sides and to find the area you multiply base times height then divide it by two.P=s+s+sA=b*h/2Perimeter and Areas
- 32.
- 33.
- 34.
- 35. To find thearea of a circle you must multiply Pi times the radius (which is the distance from the center to any point of the circumference) squared. And to find the circumference (perimeter) you must multiply 2*Pi times the radius.P= 2*Pi*rA= Pi*r^2Circle Area and Circumference
- 36.
- 37. The five stepsare: first understand the problem; second, identify the variable you need; third, draw the problem; fourth, multiply or divide the numbers that have a variable to leave it alone; and last, solve.Five Steps
- 38. I have aterrain that is 20 times 40 meters big. I would like to know the area of it. What is it?The length is 40 and width 20The variable is areaA=20*40The area of my terrain is 800m^2Example:
- 39. Translation:It’s when youslide an object in any direction.Rotation:It’s to rotate a figure around a point.Reflection:It’s to to reflect your figure across any line.Transformations
- 40.
- 41.
- 42.
- 43.