In the quadrilateral given below, AD = BC, P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus.

It is given that, In △ABD, P and Q are mid-points of AB and BD, PQ || AD and PQ = AD = BC .......(i) In △ACD, R and S are mid-points of CD and AC, RS || AD and RS = AD = BC .......(ii) In △BCD, R and Q are mid-points of CD and BD, RQ || BC and RQ = BC .......(iii) In △ABC, P and S are mid-points of AB and AC, PS || BC and PS = BC .......(iv) From (i) and (ii) we get, PQ || RS From (iii) and (iv) we get, RQ || PS From (i), (ii), (iii) and (iv) we get, PQ = RS = PS = RQ. Since, all sides are equal and opposite sides are parallel. Hence, proved that PQRS is a rhombus.

In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that
(i) G is midpoint of BC
(ii) 2EG = AB + CD

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In the quadrilateral given below, AB || DC. E and F are mid-points of non-parallel sides AD and BC respectively. Calculate :
(i) EF if AB = 6 cm and DC = 4 cm
(ii) AB if DC = 8 cm and EF = 9 cm.

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In the figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :
(i) ∠EFG = 90°
(ii) The line drawn through G and parallel to FE bisects DA.

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In the adjoining figure, the lines l, m and n are parallel to each other, and G is mid-point of CD. Calculate :
(i) BG if AD = 6 cm
(ii) CF if GE = 2.3 cm
(iii) AB if BC = 2.4 cm
(iv) ED if FD = 4.4 cm

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Mathematics

In the quadrilateral given below, AD = BC, P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus.

Mid-point Theorem

Related Questions

In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that
(i) G is midpoint of BC
(ii) 2EG = AB + CD

In the quadrilateral given below, AB || DC. E and F are mid-points of non-parallel sides AD and BC respectively. Calculate :
(i) EF if AB = 6 cm and DC = 4 cm
(ii) AB if DC = 8 cm and EF = 9 cm.

In the figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :
(i) ∠EFG = 90°
(ii) The line drawn through G and parallel to FE bisects DA.

In the adjoining figure, the lines l, m and n are parallel to each other, and G is mid-point of CD. Calculate :
(i) BG if AD = 6 cm
(ii) CF if GE = 2.3 cm
(iii) AB if BC = 2.4 cm
(iv) ED if FD = 4.4 cm

Mathematics

In the quadrilateral given below, AD = BC, P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus.

Mid-point Theorem

Related Questions

In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that(i) G is midpoint of BC(ii) 2EG = AB + CD

In the quadrilateral given below, AB || DC. E and F are mid-points of non-parallel sides AD and BC respectively. Calculate :(i) EF if AB = 6 cm and DC = 4 cm(ii) AB if DC = 8 cm and EF = 9 cm.

In the figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :(i) ∠EFG = 90°(ii) The line drawn through G and parallel to FE bisects DA.

In the adjoining figure, the lines l, m and n are parallel to each other, and G is mid-point of CD. Calculate :(i) BG if AD = 6 cm(ii) CF if GE = 2.3 cm(iii) AB if BC = 2.4 cm(iv) ED if FD = 4.4 cm

In the quadrilateral given below, AB || DC || EG. If E is mid-point of AD, prove that
(i) G is midpoint of BC
(ii) 2EG = AB + CD

In the quadrilateral given below, AB || DC. E and F are mid-points of non-parallel sides AD and BC respectively. Calculate :
(i) EF if AB = 6 cm and DC = 4 cm
(ii) AB if DC = 8 cm and EF = 9 cm.

In the figure given below, ABCD is a kite in which BC = CD, AB = AD. E, F, G are mid-points of CD, BC and AB respectively. Prove that :
(i) ∠EFG = 90°
(ii) The line drawn through G and parallel to FE bisects DA.

In the adjoining figure, the lines l, m and n are parallel to each other, and G is mid-point of CD. Calculate :
(i) BG if AD = 6 cm
(ii) CF if GE = 2.3 cm
(iii) AB if BC = 2.4 cm
(iv) ED if FD = 4.4 cm