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Given: AC bisects angle BCD , Angle ABC is congruent to angle ADC prove AB is congruent to AD. Help immediately

Sagot :

msm555

Answer:

Solution given;

<BCA=<ACD

<ABC=<ADC

now

In traingle ABC & ∆ ACD

AC=AC[common base]

<BCA=<ACD[bisector bisect it]

<ABC=<ADC[Given]

∆ABC is congruent to ∆ ACD by S.A.A. axiom

AB is congruent to AD.

[ corresponding sides of a congruent triangle are equal]

Hence proved.

View image msm555

Opposite sides of ∠BAC and ∠CAD is equal BC = DC .

Therefore,  AB is congruent to AD.

Given that,

AC bisects angle BCD ,

Angle ABC is congruent to angle ADC

We have to prove,

AB is congruent to AD.

According to the question,

AC bisects ∠BCD,

Angle ABC is congruent to angle ADC

Then, In triangle ABC & ∆ ACD

AC =AC [common base in the triangle]

<BCA = <ACD [bisector bisect it]

<ABC = <ADC [Given]

If one angle between two adjacent sides of a triangle is similar to angle between two sides of another triangle then two triangles are congruent is called SAS-Congruence-Axiom.

Then,

By SAS-Congruence-Axiom

∆ABC is congruent to ∆ACD  

AB is congruent to AD.  [corresponding sides of a congruent triangle are equal]

Then,

BC (opposite side of ∠BAC) = DC (opposite side of ∠CAD),

BC = DC

Opposite sides of ∠BAC and ∠CAD is equal BC = DC .

Therefore,  AB is congruent to AD.

Hence proved.

To know about Triangles click the link given below.

https://brainly.com/question/668486

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