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Parameters of Triangles (Sides and Angles)

Let A B and C...

Question

Let and be two parallel lines and be a transversal. Let intersect in L. suppose the bisector of ∠ALP intersect in R and the bisector of ∠PLB intersect in S. Prove that ∠LRS + ∠RSL = 90°

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Solution

The corresponding figure can be drawn as:

AB is a straight line

Now, in triangle RLS:

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Similar questions

\leftrightarrow A B

\leftrightarrow C D

be two parallel lines and

\leftrightarrow P Q

be a transversal. Let

\leftrightarrow P Q

\leftrightarrow A B

in L. Suppose the bisector of

∠ A L P

\leftrightarrow C D

in R and the bisector of

∠ P L B

\leftrightarrow C D

in S. Prove that

∠ L R S + ∠ R S L = 90^{o}

Q. In Fig., AB and CD are parallel lines intersected by a transversal PQ at L and M respectively. If ∠LMD = 35° find ∠ALM and ∠PLA.

Let AB and CD be two line segments such that AD and BC intersect at O. Suppose AO = OC and BO = OD. Prove that AB = CD.

\leftrightarrow A B

\leftrightarrow C D

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\to O P

be the bisector of

∠ B O D

\to O Q

be the bisector of

∠ A O C

Q, O, P

Let and be two parallel lines and be a transversal. Show that the angle bisectors of a pair of two internal angles on the same side of the transversal are perpendicular to each other.

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