In the given figure , D , E , F are respectively the mid-points if the sides AB , BC and CA of ∆ABC.Prove that ADEF is a parallelogram
Answers
ADEF is a parallelogram
Step-by-step explanation:
Given ABC is a triangle.
D,E and F are midpoints of sides AB, BC and CA respectively.
To prove ADEF is a parallelogram:
In ΔABC,
F is the midpoint of AC and E is the midpoint of BC.
Line segments joining the midpoints of two sides of a triangle is parallel to the third side.
∴ FE || AB.
Parts of parallel lines are parallel.
⇒ FE || AD --------- (1)
Similarly,
D is the midpoint of AB and E is the midpoint of BC.
Line segments joining the midpoints of two sides of a triangle is parallel to the third side.
∴ DE || AC.
Parts of parallel lines are parallel.
⇒ DE || AF --------- (2)
From (1) and (2),
FE || AD and DE || AF
In ADEF, both pairs of opposite sides are parallel.
∴ ADEF is a parallelogram.
To learn more...
1. In the given figure D, E, Fare respectively the midpoints of the sides AB, BC and CA of triangle ABC prove that ADEF is the parallelogram
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2. In triangle ABC, D, E and F are the mid points of sides AB, BC and CA respectively. show that triangle ABC is divided into four congruent triangles, when three mid points are joined to each other
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Answer:
Step-by-step explanation:
ADEF is a parallelogram
Step-by-step explanation:
Given ABC is a triangle.
D,E and F are midpoints of sides AB, BC and CA respectively.
To prove ADEF is a parallelogram:
In ΔABC,
F is the midpoint of AC and E is the midpoint of BC.
Line segments joining the midpoints of two sides of a triangle is parallel to the third side.
∴ FE || AB.
Parts of parallel lines are parallel.
⇒ FE || AD --------- (1)
Similarly,
D is the midpoint of AB and E is the midpoint of BC.
Line segments joining the midpoints of two sides of a triangle is parallel to the third side.
∴ DE || AC.
Parts of parallel lines are parallel.
⇒ DE || AF --------- (2)
From (1) and (2),
FE || AD and DE || AF
In ADEF, both pairs of opposite sides are parallel.
∴ ADEF is a parallelogram.