Ok, everyone I hoped you had some very good days of rest. Now, let's start with the math. I know that this should have been posted a long time ago but my computer sort of meltdown.First of all I need to thank my cousins for fixing my computer and making me recovery disks.

Last two weeks we reviewed the questions from our circle unit. The first question was:

Given:

line AP and line AQ are tangents

Arcs BS and RE are congruent

Angles 2 and 5 are congruent

Prove that lines BC and ED are congruent

Statement and Reason

Lines AB and AE are congruent Tangent Theorem

Angles 3 and 4 are congruent Inscribed Angle Theorem

Triangles ABC and AED are congruent Angle-angle-side

LInes BC and ED are congruent From above

The second question was:

Isosceles triangle ABC is inscribed in a circle with a diameter 12 cm. Side AB is a diameter. Determine the length of BC.

Let X=the length of lines AC and BC.

Then use the phythagorean theorem

x^2+x^2=12^2 2x^2=144

x^2=72

x=√72

x=6√2

The third question was:

Quadrilateral PQRS is inscribed in a circle. Side PQ is parallel to side SR. The diagonals intersect at T. Prove that triangles TSR and TPQ are isosceles.

Statement and Reason

Arcs PS and QR are congruent Parallel Chords Theorem

Lines PT and QT are congruent Congruent chords theorem

Lines ST and RT are congruent Congruent chords theorem

TRiangles TSR and TPQ are isosceles From above

The fourth one was:

The circle with centre O has 4 points of tangencyA,B,C and D.Angle AEB =30°, angle ADC=90, and Angle DCB=85.FInd the measure of angle CDG.Statement And Reason

Angle BAD=95 Cyclic Quadrilateral Theorem

LInes EA and EB are congruent Tangent theorem

Triangle AEB is isosceles From above

Angles EAB and EBA=75 BAse Angles

LInes HD and HA are congruent Tangent theorem

Angle HAD =10 Supplementary angles

Angle HDA=10 base angles

Angle CDG=80 Supplementary angle

Then after we reviewed the test we practiced on more stuff on Logic

The first question was: A survey of 80 students showed that 45 like rock music, 25 liked country and 10 liked both. How many liked neither?

The second question was:

140 homes are surveyed 90 have a stereo, 70 have a DVD player and 40 have both. HOw many have neither?

The last question was:

150 people were surveyed on their reading preferences

90- mystery

70- history novels

45-sci-fi

30-mystery and history

25- mystery and sci-fi

22-history and scifi

10 -reads all 3

How many read

1. At least one type of book

2. Exactly one type

3 Exactly two types

4. Do not read any of the 3 types

That's it for this edition of my scribe. Again, i'm sorry for the images because my paint and RFXsoftware is not working properly eversince last year. I must admit that i need a new computer.

REMINDERS

Flicker Assignment (trigonometry)

DElicious (Put at least one link for every unit we finished)

## January 07, 2007

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