+0  
 
0
39
1
avatar

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?

 

 May 11, 2020

Best Answer 

 #1
avatar+20906 
+1

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.

 May 11, 2020
 #1
avatar+20906 
+1
Best Answer

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.

geno3141 May 11, 2020

17 Online Users

avatar
avatar