Question

1.3. In the given figure, AB = AC and BD=
DC. Prove
a. A ABD AACD
b. ADB = ADC = 90°
c. ZB= 4C
d. BAD = Z CAD
​

Answer 1

Answer:

Step-by-step explanation:

A) In Δ ABD AND Δ ACD

AB=AC {GIVEN}

BD=DC {GIVEN}

AD=AD {COMMON SIDE}

SO BY SSS (SIDE-SIDE-SIDE) CONGRUENCE CRITERIA

ΔABD≅ACD HENCE PROVED

B) ΔABD≅ACD BY SSS CRITERIA {PROVED ABOVE}

∠ADB=∠ADC {C.P.C.T}

∠ADB+∠ADC=180 {LINEAR PAIR}

∠ADB+∠ADB=180

2(∠ADB)=180

∠ADB=180/2

∠ADB=90

SO ∠ADB=∠ADC=90 HENCE PROVED

3) ΔABD≅ACD BY SSS CRITERIA {PROVED ABOVE}

∠B=∠C {C.P.C.T} HENCE PROVED

4) ΔABD≅ACD BY SSS CRITERIA {PROVED ABOVE}

∠BAD=∠CAD {C.P.C.T} HENCE PROVED

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