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Given that is both the median and altitude of triangle ABC, congruence postulate SAS is used to prove that triangle ABC is what type of triangle?

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Answer:

triangle ΔABC is an isosceles triangle.

Explanation:

Given : Given that is both the median and altitude of triangle ABC.

To find : congruence postulate SAS is used to prove that triangle ABC is what type of triangle.

Solution : We have given that both the median and altitude of triangle ABC.

Let AD represent both the median and altitude of triangle ABC.

A median divides the side in two equal parts.

So , BD=BC.

An altitude is a perpendicular drawn .

A perpendicular makes an angle of 90°.

Hence <ADB = <ADC = 90°

AD is the side common to both the triangles ADB and ADC.

Hence, Δ ADB≅ΔADC (SAS congruence postulate).

So AB=AC by c.p .c .t.c(congruent parts of congruent triangles are congruent)

Hence by definition of Isosceles triangle ΔABC is an isosceles triangle.

Therefore, triangle ΔABC is an isosceles triangle.

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