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  1. Write a paragraph proof for the following conjecture. Given: bisects . . Prove: is a right triangle. Answer: Angle PQR equals 90 degrees Given:

Write a paragraph proof for the following conjecture. Given: bisects . . Prove: is a right triangle. Answer: Angle PQR equals 90 degrees Given: class=

Verified Answer :

if pqs is 45 degrees then sqr is 45 degrees by the definition of a bisector. pqs is equal to sqr becuase of definition of congruent angles therefore pqs + sqr= 90 by the addition property. what this means is that pqr is a right angle because of the definition of a right angle

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Answer with Step-by-step explanation:

We are given that in triangle PQR

QS bisect the angle PQR

\(\angle PQS=45^{\circ}\)

We have to prove that \(\angle PQR=90^{\circ}\)

\(\angle PQS=\angle PQR\)

Because QS bisect the angle PQR.

Therefore, \(\angle PQR=45^{\circ}\)

\(\angle PQR=\angle PQR+\angle PQS\)

Substitute the values then we get

\(\angle PQR=45+45\)

\(\angle PQR=90^{\circ}\)

Hence, triangle PQR is right triangle because one angle of triangle is of 90 degrees.

Hence, proved.

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