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?

Guest May 11, 2020

#1**+1 **

Since AC = BC, triangle(ABC) is an isosceles right triangle. Therefore, angle(B) is a 45^{o} 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**.

geno3141 May 11, 2020

#1**+1 **

Best Answer

Since AC = BC, triangle(ABC) is an isosceles right triangle. Therefore, angle(B) is a 45^{o} 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**.

geno3141 May 11, 2020