6.1-Terms and Definitions

6.1-Terms and Definitions Important Formulae

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Grade 9 → Math → Lines and Angles → 6.1-Terms and Definitions

After successful completion of this topic, you should be able to:

  • Understand various types of angles.

Axiom 6.1 : If a ray stands on a line, then the sum of two adjacent angles so formed is 180°.
Axiom 6.2 : If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line.
Theorem 6.1 : If two lines intersect each other, then the vertically opposite angles are equal.


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In Fig. 6.13, lines AB and CD intersect at O. If ∠ AOC + ∠ BOE = 70° and ∠ BOD = 40°, find ∠ BOE and reflex ∠ COE.

In Fig. 6.14, lines XY and MN intersect at O. If ∠POY = 90° and a:b = 2:3, find c.

In Fig. 6.15, ∠ PQR = ∠ PRQ, then prove that ∠PQS=∠PRT.

In Fig.6.16, if x+y = w+z, then prove that AOB is a line.

In Fig. 6.17, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that: ∠ROS = $\dfrac{1}{2} (∠QOS – ∠POS)$.

It is given that ∠ XYZ = 64° and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ ZYP, find ∠ XYQ and reflex ∠ QYP.