Q12 of 16 Page 88

Let’s prove if one angle of a parallelogram is right angle, then all other angles of the parallelogram are also right angles.


Given ABCD is a parallelogram in which AB||CD and BC||AD.


∠A=90°


Since, DC||AB,


∠D+∠A=180° (co-interior angles)


⇒ ∠D+90°=180°


⇒ ∠D=180°-90°


⇒ ∠D=90°…………..(1)


Since, AD||BC,


∠B+∠A=180° (co-interior angles)


⇒ ∠B+90°=180°


⇒ ∠B=180°-90°


⇒ ∠B=90°…………..(2)


Also, ∠D+∠C=180° (co-interior angles)


⇒ ∠C+90°=180° (from(1))


⇒ ∠C=180°-90°


⇒ ∠C=90°…………..(3)


Hence, if each angle of a parallelogram is 90° then all the other angles of the parallelogram are 90°.


More from this chapter

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8

In the figure beside PQ||RS, ∠BPQ=40°, ∠BPR=155° and ∠CRS=70°; let’s write the measurement of all the angles of APR


 9

O is any point inside two parallel lines AB and CD. OP and OQ are two perpendiculars on AB and CD respectively. Let’s prove that P,O and Q are collinear.

 10

Each pair of arms of two angles is parallel to each other. Let’s prove either these angles are equal in measurement or they are supplementary.

 11

The diagonal AC of the parallelogram ABCD bisects ∠BAD. Let’s prove that the diagonal AC also bisects ∠BCD.