Q17 of 45 Page 164

Consider two parallel lines and a transversal. Among the measures of 8 angles formed, how many distinct numbers are there?

4.JPG


AB and CD are two parallel lines.


EF is the transversal, which cuts AB at G and CD at H.


Here, ∠AGE = ∠BGH [Vertically opposite angle]


∠AGE = ∠GHC [Corresponding angle]


∠GHC = ∠FHD [Vertically opposite angle]


∴ ∠AGE = ∠BGH = ∠GHC = ∠FHD


Similarly, ∠BGE = ∠AGH [Vertically opposite angle]


∠BGE = ∠GHD [Corresponding angle]


∠GHD = ∠FHC [Vertically opposite angle]


∴ ∠BGE = ∠AGH = ∠GHD = ∠FHC


So, we have only 2 distinct values.


More from this chapter

All 45 →
13

Let be a ray and let and be two rays on the same side of , with between and . Let be the bisector of ∠AOB. Prove that

∠XOA + ∠XOB = 2∠XOC

 14

Let and be two rays and let be a ray between and such that ∠AOX >∠XOB. Let OC be the bisector of ∠AOB.

∠AOX – ∠XOB = 2∠COX

 15

Let be three rays such that lies between and . Suppose the bisectors of ∠AOC and ∠COB are perpendicular to each other. Prove that B, O, A are collinear.

 16

In the adjoining figure,

Prove that


∠ABC – ∠DCB + ∠CDE = 180°.