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prove that the sum of the measures of the interior angles of a triangle 180 degrees be sure to create and name in the appropriate geometric figures

Respuesta :

rebellalancy8

Answer:


Step-by-step explanation:

if ABC is a triangle then <]ABC + <}BCA +<}CAB = 180 degrees

Poof:

Draw line a through points A and B. Draw line B through point C and parallel to line a

Since line 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 quadrilateral and <)CAB = <}DCA then AB and DC are parallel.

Step-by-step explanation:

Consider a triangle ABC and let ∠A + ∠B + ∠C = 180°

Construct a straight line DE running parallel to BC and passing though A.

Now let

∠BAC = 1

∠ABC = 2

∠ACB = 3

∠DAB = 4

∠EAC = 5

Therefore we know that

∠DAB = ∠ABC (alternate angles), so 4 = 2

∠EAC = ∠ACB (alternate angles), so 5 = 3

Now line CE is straight line and we know that angle for a straight line 180°.

Thus ∠DAB + ∠BAC + ∠EAC  = 180°

or      ∠ABC + ∠BAC + ∠ACB =  180°

or          ∠A + ∠B + ∠C = 180°

Thus proved.

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