ANGLE PROOFS CONCEPT 15 Def of Congruent Angles

Def. of Congruent Angles Angle Addition Postulate Def. of Supplementary Angles Definition of Bisector

Linear Pair Theorem Right Angle Congruence Theorem Congruent Supplements Theorem Congruent Complements Theorem

Statements 1. 2. 6. Reasons 1. Given 2. Angle addition post. 3. Given

Statements 1. Reasons 1. Given 2. Def. of right angle 3. Angle Addition

Statements 3. 4. Reasons 1. Given 2. Def. of right angle 3. Substitution

Statements 3. 4. 7. Reasons 1. Given 2. Given 3. Def. of Supplementary

Statements 3. 4. Reasons 1. Given 2. Given 3. Def. of Complementary 4.

Statements 2. 3. 4. Reasons 1. Given 2. Def of perpendicular 3. Right

Statements Reasons 1. Givens 2. 3. 4. 5. 6. 7. 8. Def. of

Statements 1. 4. Reasons 1. Given 2. Given 3. Linear Pair Theorem 4.

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ANGLE PROOFS CONCEPT 15

Def. of Congruent Angles Angle Addition Postulate Def. of Supplementary Angles Definition of Bisector Def. of Perpendicular Lines Vertical Angles Theorem Def. of Right Complementary Angles

DEFINITION OF CONGRUENT ANGLES

ANGLE ADDITION POSTULATE

DEFINITION OF ANGLE BISECTOR

DEFINITION OF COMPLEMENTARY ANGLES

DEFINITION OF SUPPLEMENTARY ANGLES

VERTICAL ANGLES THEOREM 2 1

DEFINITION OF PERPENDICULAR LINES

DEFINITION OF RIGHT ANGLES

Linear Pair Theorem Right Angle Congruence Theorem Congruent Supplements Theorem Congruent Complements Theorem

Statements 1. 2. 6. Reasons 1. Given 2. Angle addition post. 3. Given Linear Pair Theorem If two angles form 4. Def. of straight angle a linear pair, then 5. Substitution Property they are 6. Def. of Supplementary Angles supplementary.

Statements 1. Reasons 1. Given 2. Def. of right angle 3. Angle Addition Postulate 4. Substitution Property 5. Def. of Complementary If the noncommon sides of two adjacent angles form a right angle, then the angles are

Statements 3. 4. Reasons 1. Given 2. Def. of right angle 3. Substitution Property 4. Def. of congruent angles Right Angle Congruence Theorem All right angles are congruent.

Statements 3. 4. 7. Reasons 1. Given 2. Given 3. Def. of Supplementary 4. Def. of Supplementary 5. Substitution Property 6. Subtraction Property 7. Def. of Congruent Ang. Congruent Supplements Theorem If two angles are supplementary to the same angle, then they are congruent.

Statements 3. 4. Reasons 1. Given 2. Given 3. Def. of Complementary 4. Def. of Complementary 5. Substitution Property 6. Subtraction Property 7. Def. of Congruent Ang. Congruent Complements Theorem If two angles are complementary to the same angle, then they are

Statements 2. 3. 4. Reasons 1. Given 2. Def of perpendicular 3. Right Angle Congruence Thm If lines are 4. perpendicular then they form congruent adjacent angles.

Statements Reasons 1. Givens 2. 3. 4. 5. 6. 7. 8. Def. of Congruent Angles Def. of Supplementary Substitution Prop. Distributive Prop. Division Prop. Substitution Prop. Definition of right angles If two angles are congruent and supplementary, then each angle is a right angle.

Statements 1. 4. Reasons 1. Given 2. Given 3. Linear Pair Theorem 4. If two angles are congruent and supplementary, then each angle is a right angle. If two congruent angles form a linear pair, then each angle is a right angle.