Question

The figure below shows a circle with center O. Segment PQ is tangent to the circle at P and segment RQ is a tangent to the circle at R.
A flowchart proof with a few blank boxes shows that angle ROQ is congruent to angle POQ.

Answer 1

Which statement and reason is most appropriate for box 4?
Answer

Triangle OPQ is similar to triangle ORQ by the side-side-side triangle similarity theorem.

Triangle OPQ is similar to triangle ORQ by the side-angle-side triangle similarity theorem.

Triangle OPQ is congruent to triangle ORQ by the side-angle-side triangle congruence theorem.

Triangle OPQ is congruent to triangle ORQ by the hypotenuse-leg triangle congruence theorem.

Answer 2

since the three boxes before the one it is asking me about are blank to im having a hard time...

Answer 3

hey i think the angle ORQ and OPQ should swap places might be a typo

Answer 4

oooh could be ive had a few of those with this class but where do you see that?

Answer 5

erm for the flow chart, segment OP is perpendicular to PQ, so it should be angle OPQ=90. same for the other box. anyway for this question the answer would be the last choice. as both the angles OPQ and ORQ are 90, we will need to consider the hypotenuse congruence theorem. as PQ and QR are the tangent of the circle, so PQ =QR. OP=OR as both are radius of circle. so the answer is Triangle OPQ is congruent to triangle ORQ by the hypotenuse-leg triangle congruence theorem. You need to remember that as long as there are 90 angle involve, apply this theorem.

Answer 6

ate and then had to draw it out again sorry but i see what you talking about thank-you!

Answer 7

ate? you're welcome. :) drawing makes things clearer. For both the triangles, they share 1 same side, PQ=QR, OP=OR and they both have 90 degrees angle. we can actually see that it's SSS or SAS etc. but remember that when right angle is involved, we will use the hypotenuse theorem.

Answer 8

yeahh, and i ate lunch aha =)

Answer 9

Haha take it easy. :) it's quite a headache to solve questions involving circles, triangles etc as there are lots of properties to memorize. practice more and you will master it 1 day.

Answer 10

i hope so!! =)