Question

please reply it is argent​

Answer 1

Answer:

i) AD = AD ( comman )

BD = CD (AD bisects BC in two equal halves )

/_ ADB = /_ ACD ( perpendicular bisector )

ii) yes, /\ ABD is congurent to /\ACD ( By SAS Congurence )

iii) yes BD = BC Because AD bisects BC in two equal parts.

Step-by-step explanation:

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Answer 2

Answer:

• ∠A is bisected by AD
• AD ⊥ BC
• ∆ADB ≅ ∆ADC ???
• ∆BD = DC ???

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$\displaystyle\underline{\bigstar\:\textsf{According to the given Question :}}$

In ∆ABD & ∆ADC

• The three pairs of matching parts will be,

$\displaystyle\sf :\implies \angle BAD = \angle CAD\:\:\bigg\lgroup AD \ bisect \angle A\bigg\rgroup$

$\displaystyle\sf :\implies AD = AD \:\:\bigg\lgroup Common \bigg\rgroup$

$\displaystyle\sf :\implies \angle BDA = \angle CDA\:\:\bigg\lgroup AD \perp BC\bigg\rgroup$

• If two triangles have three parts matching then they are called as congruent triangles, that is when we place then on top of each other they will fit together perfectly
• There are various criteria for congruency like,some are below

1. ASA : Angle Side Angle
2. SSS : Side Side Side
3. SSA : Side Side Angle

$\displaystyle\therefore\pink{\sf\triangle ABD \cong \triangle ADC}\:\:\bigg\lgroup\sf ASA\bigg\rgroup$

• If two triangles are congruent then all their sides and their sides will be equal

$\displaystyle\sf \dashrightarrow BD = DC \:\:\bigg\lgroup CPCT\bigg\rgroup$

$\displaystyle\therefore\:\underline{\textsf{\textbf{ Hence Proved!! }}}$