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Let triangle ABC be an isosceles triangle where angle ABC is congruent to angle BCA. Prove that the sides (AB and AC) opposite the congruent base angles of a triangle are congruent.

I constructed line AD as a perpendicular bisector of line BC. Angles BDA and CDA are both 90 degrees because of the construction of a perpendicular bisector. Angles BDA and CDA are congruent because of the transitive property of equality. Line BD is also equal to CD according to the definition of a perpendicular bisector. Triangles ABD and ACD are congruent by the angle side angle postulate. Since the parts of the congruent triangles are congruent, lines AB and AC are congruent.

KarpaT KarpaT · Answer 2 · 2022-07-05T14:17:19+02:00

The sides AB and AC opposite the congruent base angles of a triangle are congruent.

What is an isosceles triangle?

An isosceles triangle is a triangle with (at least) two equal sides. A polygon that consists of two equal sides, two equal angles, three edges, three vertices and the sum of internal angles of a triangle equal to 180°.

For the given situation,

Triangle ABC be an isosceles triangle.

∠ABC ≅ ∠BCA.

The diagram below shows an isosceles triangle ABC with AD is the perpendicular bisector of BC.

The perpendicular bisector AD divides the line BC as BD and DC.

Then, BD = DC.

We get triangles ΔADB and ΔADC,

AD = AD [∵ common side]

⇒ [tex]\angle ADB = \angle ADC=90[/tex]

Thus by ASA theorem,

The two triangles ΔADB and ΔADC are similar.

Then by CPCT theorem,

Side AB ≅ AC.

Therefore the sides AB and AC opposite the congruent base angles of a triangle are congruent.

Hence we can conclude that the sides AB and AC opposite the congruent base angles of a triangle are congruent.

Learn more about an isosceles triangle here

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Please help! Let triangle ABC be an isosceles triangle where angle ABC is congruent to angle BCA. Prove that the sides (AB and AC) opposite the congruent base angles of a triangle are congruent.

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What is an isosceles triangle?

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Please help!

Let triangle ABC be an isosceles triangle where angle ABC is congruent to angle BCA. Prove that the sides (AB and AC) opposite the congruent base angles of a triangle are congruent.