State and prove exterior angle property of a triangle
Asked by admin @ in Math viewed by 293 People
State and prove exterior angle property.
Asked by admin @ in Math viewed by 293 People
State and prove exterior angle property.
Answered by admin @
Answer:
Triangle is the smallest polygon which has three sides and three interior angles. In this article, we are going to discuss the angle sum property and the exterior angle theorem of a triangle with its statement and proof in detail.
Angle Sum Property of a Triangle Theorem
In the given triangle, ∆ABC, AB, BC, and CA represent three sides. A, B and C are the three vertices and ∠ABC, ∠BCA and ∠CAB are three interior angles of ∆ABC.
Angle Sum Property of a Triangle
Theorem 1: 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←→ parallel to the side BC of the given triangle.
triangle.
Proof for Angle Sum Property of a 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°.
Step-by-step explanation:
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