In the diagram, ABC has a right angle at C, and AC = BC. If AC = AD, AB is perpendicular to DE, and CE = 7, then what is BD?
Since AC = BC, triangle(ABC) is an isosceles right triangle. Therefore, angle(B) is a 45o angle.
This makes triangle(BDE) an isosceles right triangle, with BD = DE.
Triangle(AEC) is congruent to triangle(AED) by hypotenuse-side.
This makes CE = ED.
Since CE = 7, ED = 7.
Since BD = ED, BD = 7.
Since AC = BC, triangle(ABC) is an isosceles right triangle. Therefore, angle(B) is a 45o angle.
This makes triangle(BDE) an isosceles right triangle, with BD = DE.
Triangle(AEC) is congruent to triangle(AED) by hypotenuse-side.
This makes CE = ED.
Since CE = 7, ED = 7.
Since BD = ED, BD = 7.