(Mathematics Project) angle sum property of an triangle Experimentally verify this statement
Answers
Step-by-step explanation:
TRIANGLE
Proof that the sum of the angles in a triangle is 180 degrees
Theorem
If ABC is a triangle then <)ABC + <)BCA + <)CAB = 180 degrees.
Proof
Draw line a through points A and B. Draw line b through point C and parallel to line a.
triangle
Since lines a and b are parallel, <)BAC = <)B'CA and <)ABC = <)BCA'.
It is obvious that <)B'CA + <)ACB + <)BCA' = 180 degrees.
Thus <)ABC + <)BCA + <)CAB = 180 degrees.
Lemma
If ABCD is a quadrilateral and <)CAB = <)DCA then AB and DC are parallel.
Proof
Assume to the contrary that AB and DC are not parallel.
Draw a line trough A and B and draw a line trough D and C.
These lines are not parallel so they cross at one point. Call this point E.
four sides
Notice that <)AEC is greater than 0.
Since <)CAB = <)DCA, <)CAE + <)ACE = 180 degrees.
Hence <)AEC + <)CAE + <)ACE is greater than 180 degrees.
Contradiction. This completes the proof.
Answer:
see below
Step-by-step explanation:
Aim : Verification of Angle Sum Property of a triangle
materials : card board, white sheet, black scetch, scissors, glue, scale
Procedure
1) take a card board & paste a white sheet on it
2) draw any triangle with black scetch
3) indicate its angles with marks (arc) at each of three vertices
4) cut along the indicated angle arcs with a scissors carefully
5) next draw a straight line on the remaining sheet with a scale
6) now paste the above three angle pieces touching their ends
Observation : the cut pieces exactly match a semicircle on the line drawn
Conclusion : As the angle on a straight line is 180°, hence the sum of the angles of the triangle proved to be180°.
precautions : care should be taken while drawing and cutting
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