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When an amount is entered on the left side of an account, it is a debit, and the account is said to be debited. When an amount is entered on the right side, it is a credit, and the account is said to be credited. The abbrevia tions for debit and credit are Dr. and Cr., respectively. Whether an increase in a given item is credited or debited depends on the category of the item. By convention, asset and expense increases are recorded as debits, whereas liability, capital, and income increases are recorded as credits. Asset and expenses decreases are recorded as cred its, whereas liability, capital, and income decreases are recorded as deb its. The following tables summarize the rule.



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7. An angle formed by two chords intersecting inside a circle is measured by one-half the sum of the intercepted arcs.

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:

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

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:





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Plan: When AD is drawn, /1 becomes an exterior angle of ^ADP, of which /P is a nonadjacent interior angle.

An account has a debit balance when the sum of its debits exceeds the sum of its credits; it has a credit balance when the sum of the credits is the greater. In double-entry accounting, which is in almost universal

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

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.

6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 ddd ddd, aaa aaa bbb, bbb, bbb, ddd, aaa ccc ccc, ccc, bbb

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use, there are equal debit and credit entries for every transaction. Where only two accounts are affected, the debit and credit amounts are equal. If more than two accounts are affected, the total of the debit entries must equal the total of the credit entries.

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

8c. An angle formed by two tangents intersecting outside a circle is measured by one-half the difference of its intercepted arcs.

Important!

Given: /P formed by tangents PA and PD intersecting at P, a point outside circle O. 1 AFD) To Prove: /P 5 2(AED Plan: When chord AD is drawn, /1 becomes an exterior angle of ^ADP, of which /P and /2 are nonadjacent interior angles.

PROOF:

Statements 1. Draw AD. 2. m/P m/2 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. Substitution Postulate

AFD)

9. If three angles of one triangle are congruent to three angles of another triangle, the triangles are similar.

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