Question

Ap and BQ are the bisectors of 2 alternate interior angles formed by the intersection of a transversal t with parallel lines l and m show that ApllBQ​

Answer 1

Answer:

firstly take two lines AP,BQ

draw a line intersecting naming T .

now draw angles 1,2,3,4

we know that 1=3, 2=4. alternate angle

alternate angles exist between parallel lines so these lines are parallel .

hence AP||BQ

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Answer 2

Step-by-step explanation:

Given In the figure l || m, AP and BQ are the bisectors of ∠EAB and ∠ABH, respectively.

To prove AP|| BQ

Proof Since, l || m and t is transversal.

Therefore, ∠EAB = ∠ABH [alternate interior angles]

1/2 ∠EAB = 1/2 ∠ABH [dividing both sides by 2]

∠PAB =∠ABQ

[AP and BQ are the bisectors of ∠EAB and ∠ABH] Since, ∠PAB and ∠ABQ are alternate interior angles with two lines AP and BQ and transversal AB. Hence, AP || BQ.

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