Mathematics
In the figure given below, D and E are mid-points of the sides AB and AC respectively. If BC = 5.6 cm and ∠B = 72°, compute
(i) DE
(ii) ∠ADE
Mid-point Theorem
37 Likes
Answer
(i) Since, D and E are mid-points of the sides AB and AC respectively,
∴ DE is parallel to BC and DE = = 2.8 cm. (By midpoint theorem)
Hence, DE = 2.8 cm.
(ii) Since, DE is parallel to BC.
∴ ∠ABC = ∠ADE (Corresponding angles)
⇒ ∠ADE = 72°.
Hence, ∠ADE = 72°.
Answered By
26 Likes
Related Questions
In the figure given below, D, E and F are mid-points of the sides BC, CA and AB respectively of △ ABC. If AB = 6 cm, BC = 4.8 cm and CA = 5.6 cm, find the perimeter of
(i) the trapezium of FBCE
(ii) the triangle DEF.
In the figure given below, D and E are mid-points of AB, BC respectively and DF || BC. Prove that DBEF is a parallelogram. Calculate AC if AF = 2.6 cm.
Prove that four triangles formed by joining in pairs, the mid-points of the sides of a triangle are congruent to each other.
If D, E and F are mid-points of the sides AB, BC and CA respectively of an isosceles triangle, ABC, prove that △DEF is also isosceles.