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.