ABCD is a rhombus.show that diagonal AC bisects angle A as well as angle C and diagonal BD bisects angle B as well as angle D?

sir/maam kindly tell me how to solve this question with proper steps?


Given:ABCD is a Rhombus

SO AB=BC=CD=AD

to prove:angle BAC=angle DAC

AND angle DCA=angle BCA

Solution: in triangles ADC and ABC

AB=AD (given)

CD=CB(given)

AC is common

so triangle ADC is congruent to triangle ABC

SO

angle BAC= angle DAC (cpct)

angle DCA= angle BCA (cpct)

HENCE PROVEN

  • 51

first prove triangle aod congruent to aob then use cpct
angle aoc=angle aod(each 90)

ab=ad (sides os rhombus)

ao=ao(same)

by rhs 

triangle congruent

simlarly prove boc congruent to doc then cpct 

  • 2

Given:ABCD is a Rhombus

SO AB=BC=CD=AD

to prove:angle BAC=angle DAC

AND angle DCA=angle BCA

Solution: in triangles ADC and ABC

AB=AD (given)

CD=CB(given)

AC is common

so triangle ADC is congruent to triangle ABC

SO

angle BAC= angle DAC (cpct)

angle DCA= angle BCA (cpct)

HENCE PROVEN

  • 9
What are you looking for?