ssrs barcode font free CE > ED, /1 > /2 8. CB > BD 9. ACB > ADB 10. AC > AD in Objective-C

Encoder Denso QR Bar Code in Objective-C CE > ED, /1 > /2 8. CB > BD 9. ACB > ADB 10. AC > AD

7. CE > ED, /1 > /2 8. CB > BD 9. ACB > ADB 10. AC > AD
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6. An angle inscribed in a circle is measured by one-half its intercepted arc. Case I: The center of the circle is on one side of the angle.
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Given: /A is inscribed in circle O. O is on side AC. To Prove: A/5 1BC 2 Plan: When radius OB is drawn, isosceles ^AOB is formed. /A is proved to be equal in measure to one-half central /1, which is measured by BC.
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Statements 1. Draw OB. 2. AO > OB 3. /A > /B 4. m/A m/B m/1
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Reasons 1. A straight line can be drawn between two points. 2. Radii of a circle are congruent. 3. If two sides of a triangle are congruent, the angles opposite these sides are congruent. 4. In a triangle the measure of an exterior angle equals the sum of the measures of the two adjacent interior angles. 5. Substitution Postulate 6. Halves of equals are equal. 7. A central angle is measured by its intercepted arc. 8. Substitution Postulate
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5. m/A m/A 2m/A 1 6. m/A 5 2m/1 7. / 1 8. / A BC
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1 2 BC
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Case II: The center is inside the angle.
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Given: /BAC is inscribed in circle O. O is inside /BAC. 1 To Prove: /BAC 2 BC Plan: When a diameter is drawn, /BAC is divided into two angles which can be measured by applying Case I.
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CHAPTER 16 Proofs of Important Theorems
PROOF:
Statements 1. Draw diameter AD. 2. / BAD 5
1 2 BD, 1
Reasons 1. A straight line may be drawn between two points. 2. An inscribed angle is measured by one-half its intercepted arc if the center of the circle is on one side. 3. If equals are added to equals, the sums are equal.
# 1 / DAC 5 2DC
1 2 DC
3. / BAC 5 2BD / BAC 5 2(BD 4. / BAC 5 2BC
1 2 DC )
4. Substitution Postulate
Case III:
The center is outside the angle.
Given: /BAC is inscribed in circle O. O is outside /BAC. To Prove: /BAC51BC 2 Plan: When a diameter is drawn, /BAC becomes the difference of two angles which can be measured by applying Case I.
PROOF:
Statements 1. Draw diameter AD. 2. / BAD 5
1 2 BD,
Reasons 1. A straight line may be drawn between two points.
1 2 CD
/ CAD 5
2. An inscribed angle is measured by one-half its intercepted arc if the center of the circle is on one side. 3. If equals are subtracted from equals, the differences are equal. 4. Substitution Postulate
1 3. / BAC 5 2BD
1 2 CD
/ BAC 5 2(BD
1 4. / BAC 5 2BC
7. An angle formed by two chords intersecting inside a circle is measured by one-half the sum of the intercepted arcs.
Given: /1 formed by chords AB and CD intersecting at point E inside circle O To Prove: /1 5 2(AC
Plan: When chord AD is drawn, /1 becomes an exterior angle of a triangle whose nonadjacent interior angles 1 1 are inscribed angles measured by 2 AC and 2 BD.
PROOF:
Statements 1. Draw AD. 2. m/ 1 m/A m/D
Reasons 1. A straight line may be drawn between two points. 2. The measure of an exterior angle of a triangle equals the sum of the measures of the nonadjacent interior angles. 3. An angle inscribed in a circle is measured by one-half its intercepted arc. 4. Substitution Postulate
1 1 3. /A 5 2BD, / D 5 2AC 1 4. / 1 5 2BD 1 2 AC
5 2(BD
CHAPTER 16 Proofs of Important Theorems
8a. An angle formed by two secants intersecting outside a circle is measured by one-half the difference of its intercepted arcs.
Given: /P formed by secants PBA and PDC intersecting at P, a point outside circle O. To Prove:
1 / P 5 2(AC
Plan: When AD is drawn, /1 becomes an exterior angle of ^ADP, of which /P is a nonadjacent interior angle.
PROOF:
Statements 1. Draw AD. 2. m/P m/A m/1
Reasons 1. A straight line may be drawn between two points. 2. The measure of an exterior angle of a triangle equals the sum of the measures of the nonadjacent interior angles. 3. Subtraction Postulate 4. An angle inscribed in a circle is measured by one-half its intercepted arc. 5. Substitution Postulate
3. m/P 4. / 1 5
1 2 AC, 1
/ A 5 2BD
1 2 BD
5. / P 5 2AC, /P5
1 2 (AC
8b. An angle formed by a secant and a tangent intersecting outside a circle is measured by one-half the difference of its intercepted arcs.
Given: /P formed by secant PBA and tangent PDC intersecting P, a point outside circle O. To Prove: / P 5 2(AD
Plan: When chord AD is drawn, /1 becomes an exterior angle of ^ADP, of which /P and /A are nonadjacent interior angles.
PROOF:
Statements 1. Draw AD. 2. m/P m/A m/1
Reasons 1. A straight line may be drawn between two points. 2. The measure of an exterior angle of a triangle equals the sum of the measures of the nonadjacent interior angles. 3. Subtraction Postulate 4. An angle formed by a tangent and a chord is measured by one-half its intercepted arc. 5. An inscribed angle is measured by one-half its intercepted arc. 6. Substitution Postulate
3. m/P 4. / 1 5
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