Question
If the perpendicular bisector of one side of a triangle goes through the opposite vertex, then the triangle is ____ isosceles.
- always
- never
- Sometimes
The correct answer is: always
Answer:
- Perpendicular bisector theorem
- According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.
- Step by step explanation:
- Step 1:
Let consider given figure,
Let arbitrary point C on perpendicular bisector.
In which,
CD is perpendicular bisector on AB.
Hence,
AD = DB
CD = CD (common)
ADC = BDC = 90o
So, according to SAS rule
ACD BCD
Hence,
CA = CB
So, triangle is always isosceles.
Hence proved.
- Final Answer:
Correct option A always.
Let arbitrary point C on perpendicular bisector.
In which,
CD is perpendicular bisector on AB.
Hence,
So, according to SAS rule
So, triangle is always isosceles.
Hence proved.
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