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

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.

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.

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.

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?

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

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

REMINDERS
Flicker Assignment (trigonometry)
DElicious (Put at least one link for every unit we finished)
No comments:
Post a Comment