(1) quadriateral ABED is a parallelogram (v) \( A C = D F \) 5 12 Fig. 8.22 0.5 2

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Question 9
In figure , AB ∥ DE, AB = DE, AC ∥ DF and AC = DF . Prove that BC ∥ EF and BC = EF.

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In Fig. 5, DE || AC and DF || AE. Prove that

\frac{E F}{B F} = \frac{E C}{B E}

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Δ A B C

and

Δ D E F

A B = D E, A B | | D E, B C = E F

and

B C | | E F

. Vertices

A, B

and

C

are joined to vertices

D, E

and

F

respectively. Show that
(i) quadrilateral

A B E D

is parallelogram
(ii) quadrilateral

B E F C

is a parallelogram
(iii)

A D | | C F

and

A D = C F

(iv) quadrilateral

A C F D

is a parallelogram
(v)

A C = D F

(vi)

Δ A B C ≅ Δ D E F

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In figure, AB ∥ DE, AB = DE, AC ∥ DF and AC = DF. Then, BC ∥ EF and BC = EF.

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In triangle ABC, D and E are mid-points of sides AB and BC respectively. Also, F is a point in side AC so that DF is parallel to BC.

Find the perimeter of parallelogram DBEF, if AB = 10 cm, BE = 8.4 cm and AC = 12 cm.

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