Question

anyone help me question fast......plzzz argent
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Answer 1

GIVEN :-

l is the bisector of / A so

/ PAB = / QAB ------- eq 1

BP and BQ are perpendiculars from B so,

/ APB = / AQB = 90° ------ eq 2

FIGURE :-

reffered to the attachment

TO PROVE :-

$(1) \: \rm{ \triangle \: apb \cong \triangle \: aqb}$

$(2) \rm{ \: bp = bq}$

SOLUTION :-

in ∆APB and ∆AQB ,

/ APB = / AQB ( from eq 2 )

/ PAB = / QAB ( from eq 1 )

AB = AB ( common )

HENCE BY AAS CONGRUENCY RULE

$\implies \boxed{ \rm{ \bold{ \therefore \: \: \triangle \: apb \cong \triangle \: aqb}}}$

NOW BY CPCT

$\implies \boxed{ \rm{ \bold{ \therefore \: \: bp \: = bq}}}$

HENCE PROVED

OTHER INFORMATION :-

Criteria for Congruency

The following are the criteria for the congruency of the triangles.

SSS Criteria for Congruency

• If three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

• If all sides are exactly the same, then their corresponding angles must also be exactly the same.

SAS Criteria for Congruency

• Axiom: Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

ASA Criteria for Congruency

• Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle

AAS Criteria for Congruency

• Two triangles are said to be congruent to each other if two angles and one side of one triangle are equal to two angles and one side of the other triangle.

RHS Criteria for Congruency

• If in two right triangles the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of the other triangle, then the two triangles are congruent.

• RHS stands for Right angle – Hypotenuse – Side.