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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:

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

Respuesta :

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

[tex]\angle PQS=45^{\circ}[/tex]

We have to prove that [tex]\angle PQR=90^{\circ}[/tex]

[tex]\angle PQS=\angle PQR[/tex]

Because QS bisect the angle PQR.

Therefore, [tex]\angle PQR=45^{\circ}[/tex]

[tex]\angle PQR=\angle PQR+\angle PQS[/tex]

Substitute the values then we get

[tex]\angle PQR=45+45[/tex]

[tex]\angle PQR=90^{\circ}[/tex]

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

Hence, proved.

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