In △ ABC, D is mid-point of AB and E is mid-point of BC. Calculate : (i) DE, if AC = 6.4 cm, (ii) ∠DEB, if ∠ACB = 63°.

(i) By the Midpoint Theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and is half of its length. In △ ABC, since D is mid-point of AB and E is mid-point of BC. So, DE = AC DE = x 6.4 = 3.2 cm Hence, the length of DE = 3.2 cm. (ii) Since DE is parallel to AC (by mid-point theorem), ∠DEB = ∠ACB = 63° (∵ corresponding angles of parallel lines) Hence, ∠DEB = 63°.

In the following figure, AB = AD, AC = AE and ∠BAD = ∠CAE.
Prove that : BC = ED.

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In triangle ABC, P is mid-point of AB and Q is mid-point of AC. If AB = 9.6 cm, BC = 11 cm and AC = 11.2 cm; find the perimeter of the trapezium PBCQ.

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In △ ABC, D, E and F are mid-points of sides AB, BC and AC respectively. Prove that AE and DF bisect each other.

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In a kite shaped figure ABCD, AB = AD and CB = CD. Points P, Q and R are mid-points of sides AB, BC and CD respectively.
Prove that :
(i) ∠PQR = 90°
(ii) Line through P and parallel to QR bisects side AD.

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Mathematics

In △ ABC, D is mid-point of AB and E is mid-point of BC. Calculate :
(i) DE, if AC = 6.4 cm,
(ii) ∠DEB, if ∠ACB = 63°.

Mid-point Theorem

Related Questions

In the following figure, AB = AD, AC = AE and ∠BAD = ∠CAE.
Prove that : BC = ED.

In triangle ABC, P is mid-point of AB and Q is mid-point of AC. If AB = 9.6 cm, BC = 11 cm and AC = 11.2 cm; find the perimeter of the trapezium PBCQ.

In △ ABC, D, E and F are mid-points of sides AB, BC and AC respectively. Prove that AE and DF bisect each other.

In a kite shaped figure ABCD, AB = AD and CB = CD. Points P, Q and R are mid-points of sides AB, BC and CD respectively.
Prove that :
(i) ∠PQR = 90°
(ii) Line through P and parallel to QR bisects side AD.

Mathematics

In △ ABC, D is mid-point of AB and E is mid-point of BC. Calculate :(i) DE, if AC = 6.4 cm,(ii) ∠DEB, if ∠ACB = 63°.

Mid-point Theorem

Related Questions

In the following figure, AB = AD, AC = AE and ∠BAD = ∠CAE.Prove that : BC = ED.

In triangle ABC, P is mid-point of AB and Q is mid-point of AC. If AB = 9.6 cm, BC = 11 cm and AC = 11.2 cm; find the perimeter of the trapezium PBCQ.

In △ ABC, D, E and F are mid-points of sides AB, BC and AC respectively. Prove that AE and DF bisect each other.

In a kite shaped figure ABCD, AB = AD and CB = CD. Points P, Q and R are mid-points of sides AB, BC and CD respectively.Prove that :(i) ∠PQR = 90°(ii) Line through P and parallel to QR bisects side AD.

In △ ABC, D is mid-point of AB and E is mid-point of BC. Calculate :
(i) DE, if AC = 6.4 cm,
(ii) ∠DEB, if ∠ACB = 63°.

In the following figure, AB = AD, AC = AE and ∠BAD = ∠CAE.
Prove that : BC = ED.

In a kite shaped figure ABCD, AB = AD and CB = CD. Points P, Q and R are mid-points of sides AB, BC and CD respectively.
Prove that :
(i) ∠PQR = 90°
(ii) Line through P and parallel to QR bisects side AD.