The Main Menu اPrevious اPrevious Next Represent a point A. Given that: 1) A is at equal distances from and 2) The distance of A from the origin 0 is.

Slides:



Advertisements
Similar presentations
Proving the Distance Formula
Advertisements

Warm-up Solve: 1) 2x + 1+4x +4x-11= 180 Compare greater than >, less than < or equal = 4+5___ 9 5+5__ 9 Find a number x. 6
Let’s make engineering more easy
1 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use Congruent Triangles Stage 6 - Year 11 Mathematic ( Preliminary )
SOLIDS Group A Group B Cylinder Cone Prisms Pyramids
Lecture 7: The Metric problems. The Main Menu اPrevious اPrevious Next The metric problems 1- Introduction 2- The first problem 3- The second problem.
Lecture 5: The Auxiliary projection Dr. Samah Mohamed Mabrouk
Unit 37 VECTORS. DEFINITIONS A vector is a quantity that has both magnitude and direction Vectors are shown as directed line segments. The length of the.
XAXA A YAYA P YBYB XBXB B Relative Reference Frames (Relative Coordinates Systems) P B = P A P A = P in reference frame A P B = P in reference frame B.
Lecture 8 ENGR-1100 Introduction to Engineering Analysis.
Introduction and Review Information
Lesson  Theorem 89: If two inscribed or tangent- chord angles intercept the same arc, then they are congruent.
Chapter 4 Exponents and Polynomials. The Rules of Exponents Chapter 4.1.
The Cosine Rule Can be used with ANY triangle, NOT just with right triangles!!!
Learning Letter Sounds Jack Hartman Shake, Rattle, and Read
SOLIDS To understand and remember various solids in this subject properly, those are classified & arranged in to two major groups. Group A Solids having.
The Main Menu اPrevious اPrevious Next Using the successive auxiliary projection, construct the development of the given regular oblique tetragonal prism.
Finding Areas with Trigonometry. Objectives I can use trigonometry to find the area of a triangle.
TO DRAW PROJECTIONS OF ANY OBJECT, ONE MUST HAVE FOLLOWING INFORMATION A) OBJECT { WITH IT’S DESCRIPTION, WELL DEFINED.} B) OBSERVER { ALWAYS OBSERVING.
Higher Unit 1 Distance Formula The Midpoint Formula Gradients
Pythagorean Theorem Indicator: G3a: Use Pythagorean Theorem to solve right triangle problems.
Find the missing angle ?0?0. Special Segments in Triangles.
5.5 – Use Inequalities in a Triangle. MN P Measure each side of the triangle in centimeters and each angle in degrees. Write these measurements on your.
Dilations Shape and Space. 6.7 cm 5.8 cm ? ? Find the missing lengths The second picture is an enlargement of the first picture. What are the missing.
Non Linear Arrays of charges Contents: 2-D Arrays Example Whiteboards.
Jeopardy Angle Pairs Bisecting $100 $100 $100 $100 $100 $200 $200 $200
SOLIDS To understand and remember various solids in this subject properly, those are classified & arranged in to two major groups. Group A Solids having.
SOLIDS To understand and remember various solids in this subject properly, those are classified & arranged in to two major groups. Group A Solids having.
Divide into meridian sections – Gore development
Notes Over Reflections A _______________is a change of position or size of a figure.
Lecture 1: Monge’s projection “The point”
The Theorem Of Pythagoras.  Pythagoras was a Greek Mathematician.( B.C) years old is even older than your teacher.  He was eccentric. (mad!!)
Sec. 5.5 Law of sines.
PAP: Perpendicular to HP and 45o to VP.
 Geometric mean of any n numbers is:  Find the geometric mean of the following list of numbers. A. 4, 6 B. 3, 5, 9 C. 4, 8, 10, 12.
Lesson 6 Menu 1.Determine whether the dilation is an enlargement, reduction, or congruence transformation for a scale factor of r= 2/3. 2.Determine whether.
Exercise r2 q” Q2” Q1’ 1x2 r1 Q2’ Q1” q’
Lecture 2: The straight line By Dr. Samah Mohamed Mabrouk By Dr. Samah Mohamed Mabrouk
Lecture 3: Revision By Dr. Samah Mohamed Mabrouk By Dr. Samah Mohamed Mabrouk
Transformations on the Coordinate Plane: Translations and Rotations.
World 1-1 Pythagoras’ Theorem. When adding the areas of the two smaller squares, a2a2 Using math we say c 2 =a 2 +b 2 b2b2 c2c2 their sum will ALWAYS.
13.1 The Distance and Midpoint Formulas. Review of Graphs.
Chapter 5 Unit Question How do we solve applications of equations in algebra?
Linear Functions Lesson 2: Slope of Parallel and Perpendicular Lines.
Side-Angle-Side Congruence by basic rigid motions A geometric realization of a proof in H. Wu’s “Teaching Geometry According to the Common Core Standards”
Angle A B C side angle A0A0 C0C0 B0B0 side angle Angle-Side-Angle Congruence by basic rigid motions A geometric realization of a proof in H. Wu’s “Teaching.
© T Madas.
L A C H B 1 2 Problem. Given two points A, B on the same side of line Find the point C on L such that and make congruent angles with L.
Notes Over Reflections A _______________is a change of position or size of a figure.
 If three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.  If AB = DE, BC = EF, AC.
Objective To use angles of elevation and depression to solve problems.
Objective Be able to use angle facts to solve problems in geometry.
Median, Angle bisector, Perpendicular bisector or Altitude Answer the following questions about the 4 parts of a triangle. The possible answers are listed.
EXAMPLE 1 Solve a triangle for the AAS or ASA case Solve ABC with C = 107°, B = 25°, and b = 15. SOLUTION First find the angle: A = 180° – 107° – 25° =
Manipulator Kinematics Treatment of motion without regard to the forces that cause it. Contents of lecture: vResume vDirect kinematics vDenavit-Hartenberg.
@ Dr.K.Thiyagu, CUTN Pythagoras Dr.K.Thiyagu, CUTN5.
HIGHER MATHEMATICS Unit 1 - Outcome 1 The Straight Line.
Angles: Setting up Equations
Snakes & Ladders Board Game
Theorem The area A of a triangle is
Miss Schwarz’s class rules
Triangles A polygon with 3 sides.
Applications of the Distance Formula
The General Triangle C B A.
The General Triangle C B A.
Triangles.
Parallel and Perpendicular 1/4 lines
Find the value of g. Find the value of h. 105° h g 75°
Law of Sines (Lesson 5-5) The Law of Sines is an extended proportion. Each ratio in the proportion is the ratio of an angle of a triangle to the length.
Presentation transcript:

The Main Menu اPrevious اPrevious Next Represent a point A. Given that: 1) A is at equal distances from and 2) The distance of A from the origin 0 is 8 cms 3) The point A is above and behind,. 4) The point A lies on the left hand side of at a distance 6 cms π 1 π 12 π π 2

8 L M A 1 =A 2 A3A3 // The Main Menu اPrevious اPrevious Next // K X = - 6 = AA x 12 z y O, Y is -ve, and Z is +ve y is -ve A 1 = A 2 A A

// + y y y y A A A A A A y y x x x 12 o oo zz z

O // O O x x x 12 z z z

The Main Menu اPrevious اPrevious Next m1m1 m3m3 m2m2 x 12 o y z

o o o z x x x 12 z z

..

The Main Menu اPrevious اPrevious Next 1 H

3 m 3 m m1m1 m2m2 H2H2 H=H1H1 V1V1 V=V2V2 S1S1 S= S3S3 S2S2 H V 3

The Main Menu اPrevious اPrevious Next o m1m1 m3m3 m2m2 x 12 y z H2H2 H3H3 V2V2 V3V3 S1S1 S2S2 S3S3 V 1 =V

m m m S S S H H H LOCUS OF A A A A R= 4

m m m x 12 V V HH S S 45

. H.

A B A B B A B A B A B A x z y O T.L A 2 B z z B B B A A A y y x x π π π z A A A z B B B y y x x 2 α β α β 1

A3A3 A1A1 A2A2 B1B1 B3B3 B2B2 m1m1 m3m3 m2m2 x 12 o y z yByB yAyA T.L[A] [B] yAyA yByB zBzB zAzA T.L [A] [B] zAzA zBzB xAxA xBxB xAxA xBxB [A] [B] T. L β α

The Main Menu اPrevious اPrevious Next B1B1 A3A3 A1A1 A2A2 B3B3 B2B2 m1m1 m3m3 m2m2 [B] [A] [B] T.L

The Main Menu اPrevious اPrevious Next There are three right angled triangles which are frequently used in solving problems in PROJECTION ; T. L Horizontal projection T. L Side projection Vertical projection

B1B1 A2A2 A1A1 B2B2

T. L of AB 1 Locus of c 1 x 12 A2A2 B2B2 0 B1B1 A1A1 T. L of BC T. L of AC Vertical projection. of AC Vertical projection. of BC.. C2C2 C1C1 / / // T. L of AC A C 2 / T. L of BC B C 2 2 //