In the figer DEF is an isosceles triangle if DM=DN then prove that MN palral EF .
Answers
DEF is an isosceles triangle if DM=DN then it is proved that MN // EF.
Step-by-step explanation:
It is given that,
DM = DN …… (i)
DEF is an isosceles triangle
i.e., DE = DF …….. [since the length of two sides of an isosceles triangle is equal] … (ii)
Join the points M and N.
Now, from (i), we have
DE = DF
⇒ DM + ME = DN + NF ….. [from the figure attached below]
⇒ DM + ME = DM + NF …… [from (i)]
⇒ DM + ME – DM = NF
⇒ ME = NF …… (iii)
From (i) and (iii), we get
Point M is the midpoint of side DE and point N is the midpoint of side DF
We know that according to the Triangle Midsegment Theorem if we join the midpoints of the two sides of the triangle then the line segment joining the midpoints will be parallel to the third side.
∴ MN // EF
Hence proved
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Prove that the triangle formed by joining the midpoints of an isosceles triangle is also an isosceles triangle.
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ABC is an isosceles triangle with AB = AC and let D, F, E be the mid-points of BC, CA and AB respectively. Show that AD is perpendicular to EF and AD bisects EF.
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Step-by-step explanation:
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