Q1 of 49 Page 13

Given below are some triangles and lengths of line segments. Identify in which figures, ray PM is the bisector of ∠OPR.

Theorem: The bisector of an angle of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

Therefore, we’ll find the ratio for all the triangle.Hence, for


(1)


= 2.33


And


= 2.33


⇒


⇒ In (1), ray PM is a bisector.


(2)


= 0.75


And


= 0.7


⇒


⇒ In (2), ray PM is not a bisector.


(3)


= 1.1


And


= 1.11


⇒


⇒ In (3), ray PM is a bisector.


More from this chapter

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4

In adjoining figure, AP ⊥ BC, AD || BC, then find A(ΔABC) : A (ΔBCD)

 5

In adjoining figure PQ ⊥ BC, AD ⊥ BC then find following ratios.


(i)

(ii)


(iii)

(iv)

2

In Δ PQR, PM = 15, PQ = 25, PR = 20, NR = 8. State whether line NM is parallel to side RQ. Give reason.

 3

In Δ MNP, NQ is a bisector of ∠N. If MN = 5, PN = 7 MQ = 2.5 then find QP.