Question

right angle triangle abc angle b is equal to 90 degree and D is the midpoint of the hypotenuse AC prove that AC is equal to BD​

Answer 1

Step-by-step explanation:

consider two triangles ABD and BCD

AD=DC. (given)

DB=DB. (common side)

ADB=BDC. (90)

triangle ABD congruent to triangle BCD

hence AB=BC

by Pythagoras thereom

in triangle ABC

AC^2=BC^2+AB^2

=2AB^2. ( AB=BC). (1)

in triangle ABD

AB^2=AD^2+BD^2. (2)

in triangle BCD

BC^2=BD^2+DC^2. (3)

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