QB: Geometry Triangles

[contact.sumeshn]

Link to the diagram:
http://www.postimage.org/image.php?v=aV7kIn9

If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD


Explanation states that: "Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD)"

Can someone clarify as to which rule is being employed in the above stmt?

Thanks.

[adiagr]

Link to the diagram:
http://www.postimage.org/image.php?v=aV7kIn9

If angle BAD is a right angle, what is the length of side BD?

(1) AC is perpendicular to BD

(2) BC = CD


Explanation states that: "Using statements 1 and 2, we know that AC is the perpendicular bisector of BD. This means that triangle BAD is an isosceles triangle so side AB must have a length of 5 (the same length as side AD)"

Can someone clarify as to which rule is being employed in the above stmt?

Thanks.

If in any triangle a perpendicular bisector on any of the sides also passes through the vertex of triangle, the triangle is isosceles.

If in any triangle two perpendicular bisectors on any two of the sides also passes through two vertices, the triangle is equilateral.

Aditya

[tim]

AC is the perpendicular bisector by definition of course. Now we have split the diagram into two triangles, BCA and DCA. They obviously share side CA, they both have a right angle at C, and BC=DC, so the triangles are congruent by SAS..