- Amedian
- Baltitude only
- Cexterior bisector
- Dneither median nor altitude
Step-by-Step Solution
Since BD = DC, AD bisects the base, so AD is the median (it is also the altitude and angle bisector in an isosceles triangle).
Answer: A) median
If the perpendicular from the vertex A of an isosceles triangle (AB = AC) meets BC at D, then BD = DC. This shows AD is the:
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: Inequalities in a triangle
**Property 1**: In a triangle, the side opposite the LARGER angle is LONGER. (Bigger angle stretches the opposite side.)
**Property 2**: Conversely, the angle opposite the longer side is larger.
**Property 3 (Triangle Inequality)**: The sum of any two sides of a triangle is GREATER than the third side.
This means three given lengths form a triangle ONLY IF each pair sums to more than the third.
Example: Can 2, 3, 6 form a triangle? Check: 2 + 3 = 5 < 6. NO.
**Property 2**: Conversely, the angle opposite the longer side is larger.
**Property 3 (Triangle Inequality)**: The sum of any two sides of a triangle is GREATER than the third side.
This means three given lengths form a triangle ONLY IF each pair sums to more than the third.
Example: Can 2, 3, 6 form a triangle? Check: 2 + 3 = 5 < 6. NO.
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