state and prove the angle sum property of a triangle
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The sum of the measures of the interior angles of a triangle is 180. The diagram above illustrates the Triangle Angle Sum Theorem.
Proof => Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Proof: Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line
PQ
←
→
PQ↔
parallel to the side BC of the given triangle.
Since PQ is a straight line, it can be concluded that:
∠PAB + ∠BAC + ∠QAC = 180° ………(1)
SincePQ||BC and AB, AC are transversals,
Therefore, ∠QAC = ∠ACB (a pair of alternate angle)
Also, ∠PAB = ∠CBA (a pair of alternate angle)
Substituting the value of ∠QAC and∠PAB in equation (1),
∠ACB + ∠BAC + ∠CBA= 180°
Thus, the sum of the interior angles of a triangle is 180°.
Proof => Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
Proof: Consider a ∆ABC, as shown in the figure below. To prove the above property of triangles, draw a line
PQ
←
→
PQ↔
parallel to the side BC of the given triangle.
Since PQ is a straight line, it can be concluded that:
∠PAB + ∠BAC + ∠QAC = 180° ………(1)
SincePQ||BC and AB, AC are transversals,
Therefore, ∠QAC = ∠ACB (a pair of alternate angle)
Also, ∠PAB = ∠CBA (a pair of alternate angle)
Substituting the value of ∠QAC and∠PAB in equation (1),
∠ACB + ∠BAC + ∠CBA= 180°
Thus, the sum of the interior angles of a triangle is 180°.
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Answer:
Theorem 1: Angle sum property of triangle states that the sum of interior angles of a triangle is 180°. Proof: ... Thus, the sum of the interior angles of a triangle is 180°.
Step-by-step explanation:
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