In ΔABC, D and E are mid-points of AB and AC respectively.
Find: ar(ΔADE) : ar(ΔABC).

Question

In ΔABC, D and E are mid-points of AB and AC respectively. Find: ar(ΔADE) : ar(ΔABC).

KnowledgeBoat · Accepted Answer

We know that, The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of the third side. Given, In Δ ABC, D is mid-point of side AB and E is the mid-point of the side AC. DE BC and DE = BC D is mid-point of side AB. AB = 2AD Let us consider ΔADE and ΔABC ∠DAE = ∠BAC [Common angle] ∠ADE = ∠ABC [Corresponding angle are equal] ΔADE ΔABC by AA similarity. Hence, ar(ΔADE) : ar(ΔABC) = 1 : 4.

Mathematics

In ΔABC, D and E are mid-points of AB and AC respectively.
Find: ar(ΔADE) : ar(ΔABC).

Similarity

Related Questions

In the given figure, BC ∥ DE, area (ΔABC) = 25 cm², area (trap. BCED) = 24 cm² and DE = 14 cm. Calculate the length of BC.

In the given figure, DE ∥ BC and DE : BC = 3 : 5. alculate ar(ΔADE) : ar(trap. BCED).

Mathematics

In ΔABC, D and E are mid-points of AB and AC respectively.Find: ar(ΔADE) : ar(ΔABC).

Similarity

Related Questions

In the given figure, BC ∥ DE, area (ΔABC) = 25 cm2, area (trap. BCED) = 24 cm2 and DE = 14 cm. Calculate the length of BC.

In the given figure, DE ∥ BC and DE : BC = 3 : 5. alculate ar(ΔADE) : ar(trap. BCED).

In ΔABC, D and E are mid-points of AB and AC respectively.
Find: ar(ΔADE) : ar(ΔABC).

In the given figure, BC ∥ DE, area (ΔABC) = 25 cm², area (trap. BCED) = 24 cm² and DE = 14 cm. Calculate the length of BC.