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HW 2.6 Geometry Pre-AP Section 2.6 – Geometric Proof Notes ______________________________ 1. Write a justification for each step, given that BX bisects ABC and m XBC = 45º a. BX bisects ABC ______________________________________ b. ABX XBC ______________________________________ c. m ABX = m XBC ______________________________________ d. m XBC = 45º ______________________________________ e. m ABX = 45º ______________________________________ f. m ABX + m XBC = m ABC ______________________________________ g. 45º + 45º = m ABC ______________________________________ h. 90º = m ABC ______________________________________ i. ABC is a right angle ______________________________________ Fill in the blanks to complete the two-column proof. 2. Given: 1 and 2 are supplementary, and 3 and 4 are supplementary, and 2 3 Prove: 1 4 Proof: STATEMENTS 1. 1 and 2 are supplementary and REASONS 1. Given 3 and 4 are supplementary 2. _________________________________ 2. Definition of supplementary angles 3. m 1 + m 2 = m 3 + m 4 3. __________________________________ 4. 4. Given 2 3 5. m 2 = m 3 5. Definition of Congruent Angles 6. _________________________________ 6. Subtraction Property of Equality 7. 7. __________________________________ 1 4 Tell whether each statement is sometimes (S), always (A), or never (N) true. 3. An angle and its complement are congruent. _____ 4. A pair of right angles forms a linear pair. ______ 5. An angle and its complement form a right angle. ______ 6. A linear pair of angles is complementary. _______ Fill in the blanks to complete the two-column proof. 7. Given: BAC is a right angle. 2 3 Prove: 1 and 3 are complementary Proof: STATEMENTS 1. BAC is a right angle. REASONS 1. Given 2. m BAC = 90º 2. ______________________________ 3. ______________________________ 3. Angle Addition Postulate 4. m 1 + m 2 = 90º 4. Substitution of Steps 2 & 3 5. 5. Given 2 3 6. ______________________________ 6. Definition of Congruent Angles 7. m 1 + m 3 = 90º 7. ______________________________ 8. ______________________________ 8. Definition of Complementary Angles Use the given plan to write a two-column proof. 8. Given: Prove: BE CE , DE AE AB CD Plan: Use the definition of congruent segments to write the given information in terms of lengths. Then use the Segment Addition Postulate to show that AB = CD and thus AB CD . 9. Given: 1 and 3 are complementary, and 2 and 4 are complementary, and 3 4 Prove: 1 2 Plan: Since 1 and 3 are complementary and 2 and 4 are complementary, both pairs of angle measures add to 90º. Use substitution to show that the sums of both pairs are equal. Since 3 4, their measures are equal. Use the Subtraction Property of Equality and the definition of congruent angles to conclude that 1 2.
