Prove that the angles in any triangle add to 180° - Junior Cycle Mathematics - Question 6 - 2016
Question 6
Prove that the angles in any triangle add to 180°.
Diagram:
Given:
Triangle ABC.
To Prove:
|∠ABC| + |∠BAC| + |∠ACB| = 180°
Construction:
Draw line DE through A p... show full transcript
Worked Solution & Example Answer:Prove that the angles in any triangle add to 180° - Junior Cycle Mathematics - Question 6 - 2016
Step 1
Diagram:
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Answer
To illustrate the problem, draw triangle ABC with points D and E such that line DE is drawn parallel to line BC.
Step 2
Given:
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Answer
We start with triangle ABC.
Step 3
To Prove:
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Answer
We need to prove that the sum of the internal angles of triangle ABC: |∠ABC| + |∠BAC| + |∠ACB| = 180°.
Step 4
Construction:
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Answer
Draw line DE through point A parallel to line BC.
Step 5
Proof:
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Answer
Since DE is parallel to BC, we have:
|∠ABC| = |∠DAB| (corresponding angles)
|∠ACB| = |∠EAC| (corresponding angles)
The angle at point A formed by line DE is a straight angle:
|∠DAE| = 180° (straight angle)
Thus, we can express this as:
|∠DAB| + |∠BAC| + |∠EAC| = 180° (based on the fact that the sum of angles on a straight line is 180°)
Combining these gives:
|∠ABC| + |∠BAC| + |∠ACB| = 180°.
Hence, we have proven that the angles in triangle ABC add up to 180°.
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