Question

B) In A ABC, AB=AC and AD is perpendicular to BC. For proving that BD =DC we followed following steps Complete the given steps: (Write the complete steps in your notebook) In A ADB and A ADC ZAOB AB AD = A ADB 2 BD (GIVEN) AD A ADC OG C ?​

Answer 1

Answer:

Solution

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Given

AB=AC and BD=DC

To prove:

△≅△ADC

Proof:

In △ADB and △ADC, we have

AB=AC    (given)

BD=DC   (given)

AD=AD    (common)

∴ △ADB≅△ADC     [By SSS congruence property]

(i)  ∠ADB=∠ADC    (corresponding parts of the congruent triangles )       ...(1)

Now, ∠ADB+∠ADC=180o     [∵∠ADB and ∠ADC are on the straight line]

⇒∠ADB+∠ADB=180o      [from(1)]

⇒2∠ADB=180o

⇒∠ADB=2180o=90o

∴∠ADB=∠ADC=90o       [from (1)]

(ii) ∠BAD=∠CAD     (∵ corresponding parts of the congruent triangles)