Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Dessin d'enfant wikipedia , lookup
Rational trigonometry wikipedia , lookup
Multilateration wikipedia , lookup
Euler angles wikipedia , lookup
Technical drawing wikipedia , lookup
History of geometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Reuleaux triangle wikipedia , lookup
Apollonian network wikipedia , lookup
History of trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Name Date: Congruent Triangles Postulate Discovery M05 Communication -Communicate math topics using tables, graphs, diagrams, symbols, and math vocabulary 1 2 3 4 5 -Underline important information -Explain math ideas verbally and in writing using diagrams, tables, graphs and symbols. -Create mathematical theories based on given information. -Use different communication strategies to express the same math idea. -Communicate math ideas to compare or defend results. -Write given information You are a mathematician trying to disprove or agree with any of the statements below. If it cannot be disproven then it is a postulate. In order to disprove a statement you must draw the triangle so that it meets all the criteria listed but forms a different triangle. If you can draw a different triangle then write “Not Always True” on top of the triangle. If you cannot draw a different triangle then write “Always True” on top of your identical triangle. Use the protractors and ruler to take accurate measurements. 1) Write in complete sentences what will be expected of you in order to complete this assignment. AAA Postulate: Two triangles that share three pairs of congruent angles are congruent. ASA Postulate: Two triangles that share a pair of congruent sides in between two pairs of congruent angles are congruent. AAS Postulate: Two triangles that share two pairs of congruent angles that follow one pair of congruent sides are congruent. mABC = 53.13 mBCA = 36.87 B m BA = 3.00 cm C A SSA Postulate: Two triangles that share two pairs of congruent sides followed by one pair of congruent angles are congruent. SAS Postulate: Two triangles that share a pair of congruent angles in between two pairs of congruent sides are congruent. SSS Postulate: Two triangles that share three pairs of congruent sides are congruent. HL Postulate: Two right triangles that share a pair of congruent legs and a pair of congruent hypotenuses are congruent. W m UV = 3.00 cm m WU = 5.00 cm V U 2) Examine the triangles that could not be drawn any differently. Explain the reasoning why those triangles are constrained (forced to look one way.) 3) Examine the triangles that could be drawn differently. Write the reasons why you were able to draw different triangles in order to prove that the particular Postulate does not exist for each disproven triangle theorem. 4) Prove your same theories from question 3 through illustration. Create triangles with different measurements and see if your statement holds true. 5) Defend the postulates you proven to be “always true” by explaining in complete sentences why they are always true.