- A13 cm
- B16 cm
- C20 cm
- D21 cm
Step-by-Step Solution
Every point on the perpendicular bisector is equidistant from and , SAS), so cm. Perimeter cm.
Answer: C) 20 cm
Line l is the perpendicular bisector of AB (tick marks and right-angle mark at M). P lies on l, PA = 7 cm and AB = 6 cm. Find the perimeter of △PAB.
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: Why SSA is not a valid congruence criterion
If you give two sides and an angle that is NOT between them, you can sometimes draw two different triangles with those measurements. The angle-and-opposite-side combination doesn't pin down the triangle uniquely.
The ONE case it works is when the angle is a RIGHT angle and the side opposite is the hypotenuse — that's exactly the RHS criterion. So RHS is essentially 'SSA but only for right triangles, and the side has to be the hypotenuse'.
**Bottom line**: Always check the angle is INCLUDED between the two sides before quoting SAS. Otherwise you've made the classic SSA mistake.
The ONE case it works is when the angle is a RIGHT angle and the side opposite is the hypotenuse — that's exactly the RHS criterion. So RHS is essentially 'SSA but only for right triangles, and the side has to be the hypotenuse'.
**Bottom line**: Always check the angle is INCLUDED between the two sides before quoting SAS. Otherwise you've made the classic SSA mistake.
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