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Geometry Unit 5: Worksheet 19 Name:______________________________ Date: ___________________ Pd: ______ Final Proof Practice 1. Given: Prove: A B C P Q R Statements Reasons 1. 1. Given 2. 3. 2. Addition Property of Equality 3. Segment Addition Postulate 4. 4. Substitution Property of Equality 5. 5. If two segments have equal measure, then they are congruent. 2. Given: M A Prove: D P B N C Statements O Reasons 1. 1. Given 2. 3. 2. If 2 angles are congruent, then they have equal measure. 3. Addition Property of Equality 4. 4. Angle Addition Postulate 5. 6. 5. Substitution Property of Equality 6. If two angles have equal measure, then they are congruent. 3. Given: Prove: X Y Z Statements T Reasons 1. 2. 3. 1. Given 2. Reflexive Property of Equality 3. Subtraction Property of Equality 4. 4. Segment Subtraction Postulate 5. 5. Substitution Property of Equality E 4. Given: Prove: A B C D F Statements Reasons 1. 2. 1. Given 2. Definition of Linear Pair. 3. 3. If 2 angles form a linear pair, then they are supplementary. 4. If 2 angles are supplementary to congruent angles, then they are congruent. 4. 5. B Given: Prove: A Statements E F C D Reasons 2. 3. 1. Given 2. Reflexive Property of Equality 3. Addition Property of Equality 4. 4. Segment Addition Postulate 5. 5. Substitution Property of Equality 6. 6. If two segments have equal measure, then they are congruent. 1. 6. Given: Prove: 2 1 Statements 3 4 Reasons 1. 2. 1. Given 2. Definition of Linear Pair. 3. 3. If 2 angles form a linear pair, then they are supplementary. 4. If 2 angles are supplementary to congruent angles, then they are congruent. 4. 7. A Given: E bisects D Prove: F G Statements B C Reasons 1. Given 1. bisects 2. If an angle is bisected, it is divided into 2 congruent angles. 3. If two angles are congruent to the same angle, then they are congruent. OR Transitive Property of Congruence 2. 3. A C 8. Given: Prove: D B Statements E Reasons 1. 1. Given 2. 3. 2. If 2 angles are congruent, then they have equal measure. 3. Reflexive Property of Equality 4. 4. Subtraction Property of Equality 5. 5. Angle Subtraction Postulate 6. 7. 6. Substitution Property of Equality 7. If 2 angles have equal measures, then they are congruent. 9. Given: Prove: 3 2 4 1 Statements Reasons 1. Given 2. If 2 angles have equal measures, then they are congruent. 3. Definition of Vertical Angles 1. 2. 3. 4. 4. If 2 angles are vertical angles, then they are congruent. 5. 5. If 2 angles are congruent to congruent angles, then they are congruent to each other. OR Transitive Property of Congruence 6. If 2 angles are congruent, then they have equal measures. 6. G 10. Given: H R Prove: X Statements Q Reasons 1. 1. Given 2. 2. If 2 rays are perpendicular, then they form right angles. 3. If 2 angles form a right angle, then they are complementary 4. If 2 angles are complementary to the same angle, then they are congruent. 3. 4. 11. Given: Prove: 1 Statements 1. 2. 3. 4. 3 4 2 Reasons 1. Given 2. Definition of Linear Pair 3. If 2 angles form a linear pair, then they are supplementary. 4. If 2 angles are supplementary to congruent angles, then they are congruent. E D 12. Given: Prove: C 2 1 3 A B F Statements Reasons 1. 2. 1) Given 2) Definition of Vertical Angles 3. 3) If 2 angles are vertical angles, then they are congruent. 4) If two angles are congruent to the same angle, then they are congruent to each other. OR Transitive Property of Congruence 4. OR Statements 1. 2. 3. are corresponding angles 4. 5. are alternate interior angles Reasons 1. Given 2. Definition of Corresponding Angles 3. If 2 lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. 2. Definition of Alternate Interior Angles 3. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. d 13. Given: b Prove: w 1 3 4 2 Statements 1. 2. 3. 4. are same-side interior angles 5. 6. are alternate exterior angles 6 5 Reasons 1. Given 2. If the measures of two angles sum to 180Ė, then the angles are supplementary. 3. Definition of Same-Side Interior Angles 4. If 2 lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel. 5. Definition of Alternate Exterior Angles 4. If 2 lines are cut by a transversal, then alternate exterior angles are congruent. q p 14. Given: b || c b Prove: p || q c Statements 1. 2. 3. 3 2 Reasons 1. Given are corresponding angles 4. 5. 6. 4 1 are corresponding angles 2. Definition of Corresponding Angles 3. If two parallel lines are cut by a transversal, then corresponding angles are congruent. 4. If 2 angles are congruent to the same angle, then they are congruent. OR Transitive Property of Congruence 5. Definition of Corresponding Angles 6. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. OR Statements 1. 2. 3. are alternate interior angles 4. 5. 6. Reasons 1. Given are alternate interior angles 2. Definition of Alternate Interior Angles 3. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 4. If 2 angles are congruent to the same angle, then they are congruent. OR Transitive Property of Congruence 5. Definition of Alternate Interior Angles 6. If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. d 15. Given: Prove: b w 1 3 4 2 Statements 1. 2. 3. 5 Reasons 1. Given are alternate interior angles 4. 5. 6. 6 form a linear pair are supplementary 7. 8. 2. Definition of Alternate Interior Angles 3. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. 4. If two angles are congruent, then they have equal measures. 5. Definition of Linear Pair 6. If 2 angles form a linear pair, then they are supplementary. 7. If 2 angles are supplementary, then their measures add to 180Ė. 8. Substitution Property of Equality y 16. Given: d ļ y kļ y Prove: k|| d 1 2 3 4 q k Statements d Reasons 1. 1. Given 2. 2. If 2 lines are perpendicular to the same line, then they are parallel to each other.