a very nice ppt for learning theorems
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The document contains proofs of several geometric theorems: 1) Intersecting lines L and K have vertically opposite angles 1 and 2 that are equal. 2) The interior angles of any triangle sum to 180 degrees. 3) The exterior angle of a triangle is equal to the sum of the two interior opposite angles. 4) In an isosceles triangle, the base angles are equal. 5) Corresponding angles are equal when two parallel lines are intersected by a transversal. 6) Angles opposite equal sides of a triangle are equal.
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Midyear exam g7 2013
This document appears to be a mathematics exam containing 7 sections with multiple questions in each section. Some of the questions involve: decomposing numbers into prime factors; calculating greatest common divisors; simplifying and transforming fractions; performing algebraic operations; factorizing expressions; proving properties and calculating values in geometric figures involving angles, parallel and perpendicular lines, midpoints; calculating perimeters and areas of geometric shapes; and expressing values in functions. The exam covers a wide range of mathematics topics testing skills in numbers, algebra, geometry and functions.
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This document discusses finding angle measures in polygons. It provides examples of using the polygon interior angles theorem and exterior angles theorem to find the sum of interior angles, classify polygons based on interior angle sums, and find individual interior and exterior angle measures. Examples include finding the sum of interior angles of an octagon (1080°) and classifying a polygon with interior angle sum of 900° as a heptagon. It also covers using linear pairs to find exterior angles given interior angles.
2.7.1 Properties of Polygons
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The three angle bisectors of a triangle are concurrent at a single point. This is proved by first constructing the angle bisectors of any triangle. It is then shown through a series of steps using properties of similar triangles and perpendicular lines that the three angle bisectors intersect at the same point. Specifically, it is shown that two pairs of triangles are similar, meaning the corresponding parts are proportional. This implies that two of the angle bisectors are the same length. It is also shown that the triangles formed at one end of an angle bisector are right triangles. Putting this all together, it is proved that the angle measure of the angles where the bisectors meet the triangle sides are equal, meaning the bisectors intersect at a
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This document contains 26 math word problems related to geometry and calculating lengths and distances between points on a number line. The problems involve finding unknown segment lengths given relationships between various points such as one segment being twice as long as another or one point being the midpoint between two other points. Multiple choice answers are provided for each problem.
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Matematicas1.pptx convertido
1. Given a triangle ABC where angle B measures 75° and side BC measures 6 cm, calculate the length of side AC if angle A measures 21°.
2. Given triangle ABC where a = 9 cm, c = 7 cm, and angle B = 35°, calculate the length of side b.
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I. The property that the sum of the three angles of any triangle is 180 degrees is proven by drawing a parallel line through one vertex of a triangle. The angles opposite the parallel sides are equal, showing the three angles sum to 180 degrees.
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A) In a generic triangle, the sum of the three known angles is set equal to 180 degrees to solve for the unknown angle.
B) In a right triangle, the two acute angles sum to 90 degrees since one angle is 90 degrees by definition.
C) In an isosceles triangle, the two angles opposite the equal sides are set equal,
Rbse solutions for class 9 maths chapter 9 quadrilaterals ex 9.5
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Presentation1
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6001 sum of angles polygons
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3. Examples are provided of applying these formulas to specific polygons like triangles and squares.
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Matematicas1.pptx convertido
1. Given a triangle ABC where angle B measures 75° and side BC measures 6 cm, calculate the length of side AC if angle A measures 21°.
2. Given triangle ABC where a = 9 cm, c = 7 cm, and angle B = 35°, calculate the length of side b.
3. Given triangle ABC where a = 5 cm, angle A = 74.3°, angle B = 90°, and angle C = 15.7°, calculate the length of side c.
Maths
1. The document describes several basic geometric constructions including constructing the bisector of an angle, the perpendicular bisector of a line segment, constructing an angle of 60 degrees, and constructing triangles given various parameters.
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3. Six different constructions of triangles are outlined, given combinations of parameters like the base, a base angle, sums or differences of sides, or the perimeter and two base angles.
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The three points (12,-1), (6,-3), (4,3) define a circle. The lines y=1 and y=2x-1 are neither tangent nor secant to the circle. The diameter of a circle is 25 cm. Given the measures of angles A and B in terms of x, solving for x reveals they are equal. The measure of arc BC is then 72 degrees.
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Geometry is the branch of mathematics that deals with points, lines, curves, surfaces and shapes. This document provides instructions on how to divide a line segment into equal parts using a ruler, pencil, protector and compass. The example shown divides an 8cm line segment AB into 5 equal parts by first drawing 30 degree angles at A and B, then using a compass to mark 5 arcs from A and B with the same radius, and finally joining the points.
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Name polygons based on their number of sides
Classify polygons based on
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Calculate and use the measures of interior and exterior angles of polygons
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There are four types of angles: acute, obtuse, right and reflex. Angle properties include: angles at a point add to 360 degrees; angles on a straight line add to 180 degrees; vertically opposite angles are equal; corresponding angles and alternate interior angles of parallel lines are equal; interior angles of a triangle add to 180 degrees; exterior angle of a triangle equals the sum of the interior opposite angles; interior angles of polygons add up based on the number of sides, following the formula (n-2) x 180 degrees, where n is the number of sides. Regular polygons have equal interior angles that add up to the total interior angle based on the number of sides.
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The document provides information about finding the measures of angles in triangles, quadrilaterals, pentagons, and hexagons based on the number of sides. It states that the sum of interior angles in a triangle is 180 degrees. For polygons with more sides, the sum of interior angles is (n-2) * 180 degrees, where n is the number of sides. It also provides information on regular polygons, exterior angles, and using formulas to find individual angle measures.
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The document discusses classifying quadrilaterals using their coordinate graphs. It explains that to identify special types of quadrilaterals, one can use the distance and slope formulas to check if sides are parallel or congruent. An example problem classifies a quadrilateral as a square by showing its four right angles using slopes and that all four sides have equal lengths using the distance formula.
Application of Similar Triangles
Mathematical application of Similar Triangles. Word problems involving similar triangles.
Disclaimer: Some parts of the presentation are obtained from various sources. Credit to the rightful owners.
sum of angles of triangles
I. The property that the sum of the three angles of any triangle is 180 degrees is proven by drawing a parallel line through one vertex of a triangle. The angles opposite the parallel sides are equal, showing the three angles sum to 180 degrees.
II. This property can be used to calculate unknown angles of different types of triangles:
A) In a generic triangle, the sum of the three known angles is set equal to 180 degrees to solve for the unknown angle.
B) In a right triangle, the two acute angles sum to 90 degrees since one angle is 90 degrees by definition.
C) In an isosceles triangle, the two angles opposite the equal sides are set equal,
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This document contains solutions to 4 questions about constructing trapezoids with given properties. Each question provides step-by-step instructions for drawing the lines and arcs needed to form a trapezoid meeting the specified conditions for side lengths, parallel sides, or angle measures. The solutions demonstrate how to use properties of parallel lines and angles, along with techniques like marking points along lines and drawing intersecting arcs, to geometrically construct the desired trapezoids.
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The document discusses interior and exterior angles of polygons. It states that the sum of the interior angles of any convex n-gon is (n-2) * 180 degrees. The sum of the exterior angles of any convex n-gon is always 360 degrees. Examples are provided to demonstrate using these formulas to find missing angle measures in different polygons. The key points are that the interior angle sum is (n-2) * 180 and the exterior angle sum is always 360.
Angles
An angle is formed by two rays with a common endpoint called the vertex. Angles are measured in degrees and can be acute, right, obtuse, straight, or reflex depending on their measure. The protractor postulate allows pairing angles with degree measures between 0 and 180 degrees. The angle addition postulate states that if a point is within an angle, the measures of the angles on either side of it will sum to the total angle measure. Adjacent angles share a vertex and side, complementary angles sum to 90 degrees, and vertical angles are opposite angles formed by two lines and are congruent.
Presentation1
A quadrilateral is a shape with four sides, four angles, and four vertices. There are six types of quadrilaterals: trapezium, parallelogram, rectangle, rhombus, square, and kite. A parallelogram is a quadrilateral where both pairs of opposite sides are parallel. The diagonals of a parallelogram bisect each other and divide the parallelogram into two congruent triangles. Opposite sides and opposite angles of a parallelogram are equal.
Golden spiral sublime
This presentation discusses the construction of the golden spiral from the sublime triangle. It begins by introducing the sublime triangle, which is made up of sides from a regular pentagon. It then demonstrates how to construct the golden spiral by repeatedly drawing angle bisectors to generate similar, smaller triangles and using the points to lay out concentric arcs that form the spiral shape. The presentation provides step-by-step instructions on drawing the angle bisectors, finding the points, and using the points and radii to construct the golden spiral arcs.
Trigonometry worksheet
This document contains a worksheet with 7 trigonometry problems:
1) Using a 34 degree angle of depression and a cliff height of 40m, find the distance of an object from the cliff base.
2) Find the angle between the body diagonal and base of a cube with side length 5cm.
3) A boat sails N30oW for 20km; calculate how far west it is from the starting port.
4) Two men see the angle of elevation to a building's top at 30 and 60 degrees; given the height is 50m, find the distance between the men.
5) An incomplete pillar's top has a 45 degree elevation at 100m;
Obj. 20 Coordinate Proof
The student is able to prove conjectures about geometric figures on a coordinate plane using coordinate proofs. A coordinate proof uses coordinate geometry and algebra by placing a figure in the coordinate plane and using properties like slope, distances between points, and coordinates of vertices to prove statements about the figure. For example, a coordinate proof can show that the diagonals of a rectangle bisect each other by finding the midpoints of the diagonals have the same coordinates.
6001 sum of angles polygons
1. The document provides information about polygons, including definitions of terms like convex polygon and regular polygon.
2. Formulas are given for calculating the sum of interior angles of polygons with n sides (180(n-2)) and the measure of one interior and one exterior angle of regular polygons.
3. Examples are provided of applying these formulas to specific polygons like triangles and squares.
Perimeter and area
1. The document discusses formulas for calculating the perimeter and area of various shapes including rectangles, squares, rhombi, kites, and parallelograms. It provides the definitions and properties of these shapes.
2. Exercises are included for calculating perimeter and area of rectangles of given dimensions and for finding missing values of rhombi and kites when given certain measurements.
3. The key formulas presented are that the area of any shape is equal to its base times its height, and the perimeter of any shape is the sum of the lengths of its sides.
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Rbse solutions for class 9 maths chapter 9 quadrilaterals ex 9.5
Rbse solutions for class 9 maths chapter 9 quadrilaterals ex 9.5
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The document provides instructions for finding missing angles in triangles and quadrilaterals. It defines different types of angles and properties of triangles and quadrilaterals, such as the sum of interior angles in a triangle equaling 180 degrees and in a quadrilateral equaling 360 degrees. It then demonstrates using these properties to calculate missing angles when given other angle measures in example problems.
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This document discusses angle relationships in geometry. It states that vertically opposite angles are equal, corresponding angles on parallel lines are equal, alternate angles on parallel lines are equal, and the sum of cointerior angles on parallel lines is 180 degrees. It also lists tests for determining if two lines are parallel: if the alternate angles are equal, corresponding angles are equal, or cointerior angles add to 180 degrees.
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1.5 Complementary and Supplementary Angles
Some slides lifted from: http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&ved=0CEsQFjAD&url=http%3A%2F%2Fdionmath.wikispaces.com%2Ffile%2Fview%2F2.3%2BComplementary%2Band%2BSuppl.%2BAngles.ppt&ei=_wVFUbzHCa-o4AP9ooGwBQ&usg=AFQjCNF-KDyDx_yiVaUuMJMdM6yOJqHASQ&sig2=wH2TZ9xGxsHgtc4cCnn2QQ&bvm=bv.43828540,d.dmg&cad=rja
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The document discusses various properties and theorems related to triangles. It defines different types of triangles based on sides and angles. It introduces concepts like congruence of triangles and corresponding parts. It describes the four main congruence rules: SAS, ASA, AAS, and SSS. It also discusses properties like angles opposite to equal sides are equal, sides opposite to equal angles are equal, sum of angles of a triangle is 180 degrees, and theorems related to inequality of sides and angles.
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- Angle-Angle-Side (AAS) - If two angles and the non-included side of one triangle are congr
maths sample paper class 9 SA2
The document is a sample question paper for a term 2 exam. It provides instructions and questions in four sections - Section A has 8 multiple choice questions worth 1 mark each, Section B has 6 questions worth 2 marks each, Section C has 10 questions worth 3 marks each, and Section D has 10 questions worth 4 marks each. The paper covers topics in mathematics including geometry, trigonometry, probability, graphs, and algebraic equations. Students are instructed that calculators are not permitted and that some questions offer internal choice between parts.
Summative assessment -I guess papers for class-ix
Grooming at the APEX INSTITUTE is done methodically focusing on understanding of the subject, tricks of tackling the questions and above all enthusing students with self confidence, ambition and a 'never say give up' spirit. As secrets of success these are no substitutes for hard work and patience.
Chapter 10 solution of triangles
This document provides information about solving triangles using trigonometric ratios (sine rule and cosine rule) and calculating areas of triangles. It includes examples of using the sine rule and cosine rule to calculate missing side lengths and angles of triangles. It also discusses the formula for calculating the area of any triangle using sine of the angles and side lengths. Exercises are provided for students to practice applying these concepts and formulas to solve multi-step triangle problems.
Perimeter and area
1. The document discusses formulas for calculating the perimeter and area of various shapes including rectangles, squares, rhombi, kites, and parallelograms. It provides the definitions and properties of these shapes.
2. Examples are given for calculating perimeter and area of rectangles with different dimensions. Exercises are also provided for finding missing values of rhombi, kites and parallelograms given some known information.
3. The key formulas presented are that the area of any shape is equal to its base times its height, and the perimeter of any shape is the sum of the lengths of all its sides.
Congruent triangles
The document discusses various properties and theorems related to triangles. It begins by defining different types of triangles based on side lengths and angle measures. It then covers the four congruence rules for triangles: SAS, ASA, AAS, and SSS. The document proceeds to prove several theorems about relationships between sides and angles of triangles, such as opposite sides/angles of isosceles triangles being equal, larger sides having greater opposite angles, and the sum of any two angles being greater than the third side. It concludes by proving that the perpendicular from a point to a line is the shortest segment.
C2 st lecture 8 pythagoras and trigonometry handout
This document provides an overview of Pythagoras' theorem, trigonometric ratios, and formulas for working with triangles. It defines different types of triangles, introduces Pythagoras' theorem, and provides examples of using it to find missing sides of right triangles. It also defines the sine, cosine, and tangent ratios and includes examples of using trigonometric functions to find angles and sides. Finally, it presents the sine rule, cosine rule, and formulas for finding the area of various triangles.
Premier semestre g8
This document contains a multi-part math exam covering geometry, algebra, and trigonometry concepts. It includes problems involving: the relative positions of circles; properties of angles in circles; finding the nature of quadrilaterals where angles are defined in terms of variables; scientific notation; fractions; properties of isosceles and right triangles; and using symmetry and perpendicular bisectors. The exam has 6 sections and tests skills across a range of math domains.
Semana 1 geo y trigo
The document provides information about geometry and trigonometry concepts. It discusses segments of a line, harmonic division of segments, the golden section, relationships between points on a line, and exercises related to finding lengths and distances given information about points. It also covers trigonometric angles and systems for measuring angles, including the sexagesimal, centesimal, and radial systems. Conversions between these systems are discussed along with example exercises calculating angle measures in different systems.
Pythagorean Proof
The document provides a proof of the Pythagorean theorem. It constructs a right triangle ABC with sides of lengths a, b, and c. It extends the sides to form a larger square with side length a+b. This creates 4 right triangles within the larger square. Equating the total area of the larger square to the sum of the areas of the 4 triangles and the square on hypotenuse c yields a2 + b2 = c2, proving the Pythagorean theorem.
quadrilateral
This document discusses properties of quadrilaterals. It begins with definitions of different types of quadrilaterals based on the number of pairs of parallel sides they have: trapezoids have 1 pair, parallelograms have 2 pairs. It then discusses properties of parallelograms and special types of parallelograms like rectangles, rhombi, and squares. Several theorems about the properties of parallelograms are then proved, such as opposite sides being equal, opposite angles being equal, and diagonals bisecting each other.
Shivam goyal ix e
The document discusses various properties of quadrilaterals:
- It defines the six types of quadrilaterals - trapezium, parallelogram, rectangle, rhombus, square, and kite.
- It provides examples and definitions for each type.
- Several theorems regarding the properties of parallelograms are presented, including that the diagonals of a parallelogram bisect each other and that opposite sides of a parallelogram are equal.
- Additional theorems state that a quadrilateral is a parallelogram if opposite sides are equal or if opposite angles are equal.
Similar to a very nice ppt for learning theorems (20)
C2 st lecture 8 pythagoras and trigonometry handout
C2 st lecture 8 pythagoras and trigonometry handout
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二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【微信：176555708】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分→ 【关于价格问题（保证一手价格）
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
学历顾问：微信：176555708
Should Repositories Participate in the Fediverse?
Presentation for OR2024 making the case that repositories could play a part in the "fediverse" of distributed social applications
重新申请毕业证书(RMIT毕业证)皇家墨尔本理工大学毕业证成绩单精仿办理
不能毕业办理【RMIT毕业证【微信176555708】皇家墨尔本理工大学文凭学历】【微信176555708】【皇家墨尔本理工大学文凭学历证书】【皇家墨尔本理工大学毕业证书与成绩单样本图片】毕业证书补办 Fake Degree做学费单【毕业证明信-推荐信】成绩单，录取通知书，Offer，在读证明，雅思托福成绩单，真实大使馆教育部认证，回国人员证明，留信网认证。网上存档永久可查！全套服务：皇家墨尔本理工大学皇家墨尔本理工大学本科学位证成绩单真实回国人员证明 #真实教育部认证。让您回国发展信心十足#铸就十年品质！信誉！实体公司！可以视频看办公环境样板如需办理真实可查可以先到公司面谈勿轻信小中介黑作坊！
可以提供皇家墨尔本理工大学钢印 #水印 #烫金 #激光防伪 #凹凸版 #最新版的毕业证 #百分之百让您绝对满意
印刷DHL快递毕业证 #成绩单7个工作日真实大使馆教育部认证1个月。为了达到高水准高效率
请您先以qq或微信的方式对我们的服务进行了解后如果有皇家墨尔本理工大学皇家墨尔本理工大学本科学位证成绩单帮助再进行电话咨询。
国外毕业证学位证成绩单如何办理：
1客户提供办理信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：我们有专业老师帮你查询）；
2开始安排制作皇家墨尔本理工大学毕业证成绩单电子图；
3毕业证成绩单电子版做好以后发送给您确认；
4毕业证成绩单电子版您确认信息无误之后安排制作成品；
5成品做好拍照或者视频给您确认；
6快递给客户（国内顺丰国外DHLUPS等快读邮寄）。
办理新西兰奥克兰大学毕业证学位证书范本原版一模一样
原版一模一样【微信：741003700 】【新西兰奥克兰大学毕业证学位证书】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
留学学历(UoA毕业证)奥克兰大学毕业证成绩单官方原版办理
制做办理奥克兰大学学历证书＜176555708微信＞【毕业证明信-推荐信做学费单＞【微信176555708】【制作UoA毕业证文凭认证奥克兰大学毕业证成绩单购买】【UoA毕业证书】{奥克兰大学文凭购买}】成绩单，录取通知书，Offer，在读证明，雅思托福成绩单，真实大使馆教育部认证，回国人员证明，＞【制作UoA毕业证文凭认证奥克兰大学毕业证成绩单购买】【UoA毕业证书】{奥克兰大学文凭购买}留信网认证。
奥克兰大学学历证书＜微信176555708（一对一服务包括毕业院长签字,专业课程,学位类型,专业或教育领域,以及毕业日期.不要忽视这些细节.这两份文件同样重要!毕业证成绩单文凭留信网学历认证！）[留学文凭学历认证(留信认证使馆认证)奥克兰大学毕业证成绩单毕业证证书大学Offer请假条成绩单语言证书国际回国人员证明高仿教育部认证申请学校等一切高仿或者真实可查认证服务。
多年留学服务公司,拥有海外样板无数能完美1:1还原海外各国大学degreeDiplomaTranscripts等毕业材料。海外大学毕业材料都有哪些工艺呢？工艺难度主要由：烫金.钢印.底纹.水印.防伪光标.热敏防伪等等组成。而且我们每天都在更新海外文凭的样板以求所有同学都能享受到完美的品质服务。
国外毕业证学位证成绩单办理方法：
1客户提供办理奥克兰大学奥克兰大学硕士毕业证成绩单信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：我们有专业老师帮你查询）；
2开始安排制作毕业证成绩单电子图；
3毕业证成绩单电子版做好以后发送给您确认；
4毕业证成绩单电子版您确认信息无误之后安排制作成品；
5成品做好拍照或者视频给您确认；
6快递给客户（国内顺丰国外DHLUPS等快读邮寄）
— — — — 我们是挂科和未毕业同学们的福音我们是实体公司精益求精的工艺！ — — — -
一真实留信认证的作用(私企外企荣誉的见证):
1：该专业认证可证明留学生真实留学身份同时对留学生所学专业等级给予评定。
2：国家专业人才认证中心颁发入库证书这个入网证书并且可以归档到地方。
3：凡是获得留信网入网的信息将会逐步更新到个人身份内将在公安部网内查询个人身份证信息后同步读取人才网入库信息。
4：个人职称评审加20分个人信誉贷款加10分。
5：在国家人才网主办的全国网络招聘大会中纳入资料供国家500强等高端企业选择人才。
制作原版1:1(Monash毕业证)莫纳什大学毕业证成绩单办理假
退学买莫纳什大学毕业证>【微信176555708】办理莫纳什大学毕业证成绩单【微信176555708】Monash毕业证成绩单Monash学历证书Monash文凭【Monash毕业套号文凭网认证莫纳什大学毕业证成绩单】【哪里买莫纳什大学毕业证文凭Monash成绩学校快递邮寄信封】【开版莫纳什大学文凭】Monash留信认证本科硕士学历认证1:1完美还原海外各大学毕业材料上的工艺：水印阴影底纹钢印LOGO烫金烫银LOGO烫金烫银复合重叠。文字图案浮雕激光镭射紫外荧光温感复印防伪。
可办理以下真实莫纳什大学存档留学生信息存档认证：
1莫纳什大学真实留信网认证（网上可查永久存档无风险百分百成功入库）；
2真实教育部认证（留服）等一切高仿或者真实可查认证服务（暂时不可办理）；
3购买英美真实学籍（不用正常就读直接出学历）；
4英美一年硕士保毕业证项目（保录取学校挂名不用正常就读保毕业）
留学本科/硕士毕业证书成绩单制作流程：
1客户提供办理信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：我们有专业老师帮你查询莫纳什大学莫纳什大学毕业证offer）；
2开始安排制作莫纳什大学毕业证成绩单电子图；
3莫纳什大学毕业证成绩单电子版做好以后发送给您确认；
4莫纳什大学毕业证成绩单电子版您确认信息无误之后安排制作成品；
5莫纳什大学成品做好拍照或者视频给您确认；
6快递给客户（国内顺丰国外DHLUPS等快读邮寄）
— — — — — — — — — — — 《文凭顾问微信：176555708》
可查真实(Monash毕业证)西澳大学毕业证成绩单退学买
办理假西澳大学毕业证【微信176555708】购买,办理Monash成绩单,Monash毕业证制作【微信176555708】【西澳大学毕业证】，Monash毕业证购买，Monash学位证，西澳大学学位证【Monash成绩单制作】【Monash毕业证文凭 Monash本科 澳洲学历认证原版制作【diploma certificate degree transcript 】【留信网认证，本科，硕士，海归，博士，排名，成绩单】代办国外（海外）澳洲、韩国、加拿大、新西兰等各大学毕业证。 ?我们对海外大学及学院的毕业证成绩单所使用的材料，尺寸大小，防伪结构（包括：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。 文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）都有原版本文凭对照。#一整套西澳大学文凭证件办理#—包含西澳大学西澳大学毕业证成绩单学历认证|使馆认证|归国人员证明|教育部认证|留信网认证永远存档教育部学历学位认证查询办理国外文凭国外学历学位认证#我们提供全套办理服务。
一整套留学文凭证件服务：
一：西澳大学西澳大学毕业证成绩单毕业证 #成绩单等全套材料从防伪到印刷水印底纹到钢印烫金
二：真实使馆认证（留学人员回国证明）使馆存档
三：真实教育部认证教育部存档教育部留服网站永久可查
四：留信认证留学生信息网站永久可查
国外毕业证学位证成绩单办理方法：
1客户提供办理西澳大学西澳大学毕业证成绩单信息：姓名生日专业学位毕业时间等（如信息不确定可以咨询顾问：我们有专业老师帮你查询）；
2开始安排制作毕业证成绩单电子图；
3毕业证成绩单电子版做好以后发送给您确认；
4毕业证成绩单电子版您确认信息无误之后安排制作成品；
5成品做好拍照或者视频给您确认；
6快递给客户（国内顺丰国外DHLUPS等快读邮寄）。
教育部文凭学历认证认证的用途：
如果您计划在国内发展那么办理国内教育部认证是必不可少的。事业性用人单位如银行国企公务员在您应聘时都会需要您提供这个认证。其他私营 #外企企业无需提供！办理教育部认证所需资料众多且烦琐所有材料您都必须提供原件我们凭借丰富的经验帮您快速整合材料让您少走弯路。
实体公司专业为您服务如有需要请联系我: 微信176555708
成绩单ps(UST毕业证)圣托马斯大学毕业证成绩单快速办理
一比一原版制作UST毕业证【微信176555708】圣托马斯大学毕业证书原版↑制作圣托马斯大学学历认证文凭办理圣托马斯大学留信网认证,留学回国办理毕业证成绩单文凭学历认证【微信176555708】专业为海外学子办理毕业证成绩单、文凭制作，学历仿制，回国人员证明、做文凭，研究生、本科、硕士学历认证、留信认证、结业证、学位证书样本、美国教育部认证百分百真实存档可查】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
◆◆◆◆◆ — — — — — — — — 【留学教育】留学归国服务中心 — — — — — -◆◆◆◆◆
【主营项目】
一.毕业证【微信：176555708】成绩单、使馆认证、教育部认证、雅思托福成绩单、学生卡等！
二.真实使馆公证(即留学回国人员证明,不成功不收费)
三.真实教育部学历学位认证（教育部存档！教育部留服网站永久可查）
四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【微信：176555708】
◇面对父母的压力，希望尽快拿到；
◇不清楚认证流程以及材料该如何准备；
◇回国时间很长，忘记办理；
◇回国马上就要找工作，办给用人单位看；
◇企事业单位必须要求办理的
◇需要报考公务员、购买免税车、落转户口
◇申请留学生创业基金
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分→ 【关于价格问题（保证一手价格）
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才
选择实体注册公司办理，更放心，更安全！我们的承诺：可来公司面谈，可签订合同，会陪同客户一起到教育部认证窗口递交认证材料，客户在教育部官方认证查询网站查询到认证通过结果后付款，不成功不收费！
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我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
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a very nice ppt for learning theorems
- 1. L K 3 1 2
- 2. Given: To prove : Intersecting lines L and K, with vertically opposite angles 1 and 2. Construction: 1=2 Label angle 3 Proof: Straight angle Straight angle 1+3=180 2+3=180 1+3=3+2 1=2 .....Subtract 3 from both sides
- 3. 4 5 a 3 1 2 b c . 5
- 4. Given: The triangle abc with 1,2 and 3. To Prove: 1+2+3=180 Construction: Proof: Draw a line through a, Parallel to bc. Label angles 4 and 5. 1=4 and 2=5 Alternate angles 1+2+3=4+5+3 But 4+5+3=180 Straight angle 1+2+3=180 Angle sum property
- 5. a 3 1 2 4 b c Q.E.D.
- 6. Given: A triangle with interior opposite angles 1 and 2 and the exterior angle 3. To prove: 1+ 2= 3 Proof: 1+ 2+ 4=180 3+ 4=180 Angle sum property 1+ 2+ 4= 3+ 4 Straight angle 1+ 2= 3
- 7. a 3 4 b 1 2 c d
- 8. Given: The triangle abc, with ab = ac and base angles 1 and 2. To prove: 1 = 2 Construction: Draw ad, the bisector of bac. Label angles 3 and 4. Proof: consider ABD and ACD ab = ac construction 3 = 4 given ad = ad common SAS criteria ABD ACD 1 = 2 CPCT
- 9. 1 3 2 t A B P C D Q
- 10. Given: AB||CD and EFGH is a transversal. To Prove: 1 = 2 Proof : 1= 5 [1] v .o .a 5= 2 [2] corresponding angles from equation 1 and 2 we get , 1= 2
- 11. Angles opposite to equal sides of triangle are equal A B D C
- 12. Given: AB=AC To prove: B= C Construction : Draw the bisector AD of A which meets BC at D Proof: In ABD and ACD AB = AC g i v e n BAD= CAD By construction AD=AD Common => ABD = ACD SAS criteria => B = C By C.P.C.T.