Geometry Agenda. Week 1.6 Objective Grade. Lines and Angles. Practice. Angles Formed by Parallel Lines Practice Proving Lines Parallel.

Transcription

1 Name Period Geometry Agenda Week 1.6 Objective Grade Monday September 26, Tuesday September 27, Wednesday September 28, Thursday September 29, Friday September 30, Lines and Angles Practice Angles Formed by Parallel Lines Practice Proving Lines Parallel Practice Perpendicular Lines Practice Work day Pep Rally Packet due by end of class today! First Things First Average

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3 Geometry: Unit 3 Lines and Angles Practice Lines and Angles pp Name Date Period MAKE A BLOCK Using the drawing below, figure out where the stores are that your block contains If there is a Foot Locker at 6, place the following: The Church and the Super Wal-Mart at vertical angles. You favorite fast food place corresponds to the Super Walmart. Super Wal-Mart and the Home Depot are same side interior angles. Foot Locker s vertical angle is an alternate exterior angle to the Church. The High School is an alternate interior angle to Home Depot. The Gas Station corresponds to the High School. The Church and your favorite fast food place are alternate exterior angles. The Skate Park s corresponding angle is the Gas Stations vertical angle. What is where?

4 Geometry: Unit 4 Angles in Parallel Lines and Transversals Practice Angles in Parallel Lines and Transversals Pages Name Date Period Directions: Solve for x. Choose the right answer and write the letter in the box below to answer the riddle. Show me how you solved it! o Which of the following are alternate interior? 6. Classify 6 and 4. (I) (S) 3and 6 (A) 4 and 6 1and 8 (T) 2and 6 (K) Corresponding (N) Linear Pair (L) Same Side Interior (P) Alternate Interior 2. Which of the following are corresponding angles? (C) (L) 2and 3 (T) 6and 7 7 and 8 (I) 4 and 8 7. Classify 5and 8? (A) Vertical Angles (G) Alternate Interior (D) Alternate Exterior (M) Linear Pair 3. If m5 3x 7 and m3 x 3, find x. 8. Find m5. (B) 1 (D) 5 (E) 46 (G) 90 (I) 42 o (N) 138 o (R) 84 o (W) 90 o 4. Find the x if m1 8x 5 and m5 7x 50 (S) 3.67 (A) 9 (T) 55 (D) Find m6. (A) 90 o (C) 138 o (O) 84 o (S) 42 o 5. Find the x if m2 3x10 and m3 6x 35 (H) 5 (L) (S) 9 (I) Find m8. (?) 180 o (!) 138 o (.) 90 o ( ) 42 o Answer:

5 Geometry: Unit 4 Angles in Parallel Lines and Transversals 11. In Botany, many plants are classified by the veins it has on the leaves. The lines that mark the width of each space are parallel. m1 =(2x 3y) and m2 = (2x + 3y). Find x and y Complete the two-column proof of the Alternate Exterior angles theorem. Given: k j Prove: 1 2 Statements Reasons 1. k j 1. Given Vertical angle theorem Draw the following or tell why it is impossible. a) Two parallel lines are intersected by a transversal so that corresponding angles are supplementary. b) Two parallel lines are intersected by a transversal so that corresponding angles are complementary. 14. In the diagram l//m. Find the value of x y. 15. For two parallel lines and a transversal, m1 = 83. For which pair of angle measures is the sum the least? a) 1 and its supplement b) 1 and its complement

6 Geometry Unit 4 Proving Lines Parallel Practice - Proving Lines Parallel Pages Name: Date: Period: Determine if the lines are parallel. Justify your reasoning. 1. Is EB parallel to HD? 2. Is EA parallel to HC? Determine if there is enough information to prove if m n. If parallel, justify your reasoning with a postulate or theorem Determine if there is enough information to prove if a b. If parallel, justify your reasoning Use the diagram and the markings. Can you conclude that AB CD? Justify your reasoning.

7 Geometry Unit 4 Proving Lines Parallel 10. What is the converse of the following statement? If 1 2, then n m. (A) 1 2 if and only if n m (B) If 2 1, then m n. (C) 1 2 if n m (D) 1 2 only if n m 11. Complete the proof. Given: 1 and 2 are supplementary. Prove: 1 2 Statements Reasons 1. 1 and 2 are supplementary 1.? 2.? 2. Definition of Linear Pair 3.? 3. Linear Pair Theorem 4.? 4. Congruent Supplements Theorem ? 12. Find the value of x that would make To shoot the snow as far as possible, each snowmaker below is set at a 45 angle. If you know that 1 2and that ma 45 o and m 45 o, which of the following would help you prove that j k? (A) Converse of Alternate Interior Theorem (B) Corresponding Angles Postulate (C) Alternate Interior Angles Theorem (D) Converse of Corresponding Angles Postulate

8 Geometry Unit 4: Perpendicular Lines Practice - Perpendicular Lines Pages Name: Date: Period: For 1 4, use the diagram to find all the missing angle measures. 1. If m1 38, then m4? 2. m2? 3. If m6 51, then m1? 4. If m3 42, then m1? 5. Which of the following must be true if macd 90? I. BCE is a right angle. II. AE BD III. BCA and BCE are complementary. (A) I only (C) III only (B) I and II only (D) I, II, III (E) None of these 6. Which of the following is true if g h? (A) m1 m2 180 (B) m1 m2 180 (C) m1 m2 180 (D) Cannot be determined 7. The diagram shows part of a circuit board for a microchip. If you know that AB BC and BC CD, explain how you can show that 7 8.

9 Geometry Unit 4: Perpendicular Lines 8. Fill in the blanks. Given: BA BC Prove: 3 and 4 are complementary. Because BA BC, ABC is a (1), and mabc (2). Because of the (3) (4) postulate, m3 m4 m ABC. So, using the substitution property, (5) + (6) = (7). Then by definition, 3 and 4 are complementary. Find the value for x in each picture To check whether two stitches lines make up a right angle, you can count the squares. For example, the lines below are perpendicular because one goes up 8 as it goes over 4, and the other goes over 8 as it goes down 4. Explain why this makes the line perpendicular.