Inscribed Angles

Hey!

today we started class by going over the quiz. Questions 5-16 were connected to each other, so if you got one of them it was easier to get the other ones. The questions said that <2=<1 2="4x+35" 1="9x" x="6." href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhVDveC6xbSnLBYcahpc7kxbnrOZ8fcI7F8qUuCjDuT1Ky5-haxhopFh_eHjyWWUcaXHcZKoLmhpNx9tFtVOPy6NrT-fjBz6T3oRW8F2UTKun9UB7c_cnuP3qxu7xriwuJzqCBPs1VQi0/s1600-h/circles+quiz+5.png">

Many people had trouble with number 27, for that one you had to visualize a segment b (from P to A) which would form a triangle closed from P to the side. Then you could use law of sine to say that:

Sin120 over AB = Sin 30 over 6

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Then we started with the new lesson: Inscribed Angles

An inscribed angle is basically an angle whose vertex is on the circle.

Theorem 9-4

this theorem states that "If an angle is inscribed in a circle, then the measure of the angle eguals one half the measure of the intercepted arc.In the diagram shown the green angle= 63, the arc then equal 126

Theorem 9-5 states that "If two inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent."...ok, right now you to notice how both inscribed angles end up in the same arc (pink one), if they end up in the same arc and the arc is twice the size of the angle (or the angle is half the arc) then consequently they are the same size.

Theorem 9-6

this theorem states that "if an inscribed angle of a circle intercepts a semi-circle, then the angle is a right angle. This one really makes sense, in a semi-circle the arc measures 180, if the inscribed angle is half of the arc (180) then its 90 (or a right angle)

Theorem 9-7 says that "If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary" which also makes sense because if you look at an inscibed angle it is opposite an arc that added with the opposite arc (formed by the opposite inscribed angle) forms a 360 circle. (if while you read my explanation while you look at the diagram it is much less confusing)

bjss and good luck

PS: eu só queria notar como a nossa aula hoje for extremamente versátil!