Q11 of 115 Page 8

In Fig 8.113, lines AB and CD are parallel and P is any point as shown in the figure. Show that ∠ABP +∠CDP = ∠DPB.

Given that,

AB ‖ CD


Let, EF be the parallel line to AB and CD which passes through P.


It can be seen from the figure that alternate angles are equal


∠ABP = ∠BPF


∠CDP = ∠DPF


∠ABP + ∠CDP = ∠BPF + ∠DPF


∠ABP + ∠CDP = ∠DPB


Hence, proved


More from this chapter

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9

If two straight lines are perpendicular to the same line, prove that they are parallel to each other.

 10

Prove that the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.

 12

In Fig 8.114, AB||CD and P is any point shown in the figure. Prove that:

∠ABP + ∠BPD + ∠CDP = 360°


 13

Two unequal angles of a parallelogram are in the ratio 2 : 3. Find all its angles in degrees.