Home
Class 10
MATHS
In DeltaABC, AC=BC and /ACB=90^(@) then ...

In `DeltaABC`, `AC=BC` and `/_ACB=90^(@)` then prove `AB^(2)=2AC^(2)`

Text Solution

Verified by Experts

`AC=CB`……(Given)…..`(1)`
In `DeltaACB`,
`/_ACB=90^(@)` ……..(Given)
`:.` by Pythagoras theorem, `AB^(2)=AC^(2)+CB^(2)`
`:.AB^(2)=AC^(2)+AC^(2)`…….[Fromn`(1)`]
`:.AB^(2)=2AC^(2)`
Promotional Banner

Topper's Solved these Questions

  • PYTHAGORAS THEOREM

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise 3.4 (3 mark each)|9 Videos
  • PYTHAGORAS THEOREM

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise 3.5 (4 mark each)|4 Videos
  • PYTHAGORAS THEOREM

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise 3.2 (1 mark each)|6 Videos
  • PROBABILITY

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise ASSIGNEMENT 5.4|12 Videos
  • QUADRATIC EQUATION

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise CHALLENGIN QUESTIONS|2 Videos

Similar Questions

Explore conceptually related problems

In DeltaABC , seg AD bot seg BC , DB=3CD . Prove that 2AB^(2)=2AC^(2)+BC^(2) .

In triangleABC , angleA= 60^(@) prove that BC^(2)= AB^(2)+AC^(2)- AB . AC

In DeltaABC if /_BAC=90^(@) and AB=AC , then /_ABC is

In figure /_ACB=90^(@) and Prove that (BC^(2))/(AC^(2))=(BD)/(AD)

In the DeltaABC,AB=a,AC=c and BC=b , then

In ABC, if BD perp AC and BC^(2)=2ACCD, then prove that AB=AC .

Draw a triangle ABC, with AC=4cm,BC=3cm and /_C=80^(@) . Measure AB. Is (AB)^(2)=(AC)^(2)+(BC)^(2)? If not,which one of the following is true: (AB)^(2)>(AC)^(2)+(BC)^(2) or (AB)^(2)<(AC)^(2)+(BC)^(2)?

Draw a triangle ABC, with AC=4cm,BC=3cm and /_C=105^(@) . Measure AB. Is (AB)^(2)=(AC)^(2)+(BC)^(2)? If not,which one of the following is true: (AB)^(2)>(AC)^(2)+(BC)^(2) or (AB)^(2)<(AC)^(2)+(BC)^(2)?

In obtuse angled DeltaABC , /_B gt90^(@) . If seg Adbot ray CB and D-B-C , then prove that AC^(2)=AB^(2)+BC^(2)+2BC*DB .