1. Explain the main parts and uses of two kinds of proofs. Part I: Draw a line to match each term with its meaning. (5 points) Term Meaning A. Definition A statement that is assumed to be true without proof B. Postulate (axiom) A statement that has already been proven to be true C. Common notion A statement that tells exactly what something is or means D. Theorem A statement that makes sense based on another statement that has already been proven E. Corollary A statement that is not officially defined but that is understood to be common sense. In an indirect proof, you prove an "if-then" statement is true by assuming the statement is false (stating the inverse or converse), and then disproving the false statement. You want to prove the statement shown below in an indirect proof. What statement should you prove is false? (1 point) Statement to Prove True: If a figure has exactly three sides, then it is a triangle. Statement to Prove False: 2. Find AB, BC, and AC. Part I: The length of line segment AC is 8x- 9. Use the figure below to find the value of x. Show your work. (1 point) 3x + 1 4x - 5 A CPart II: Find a Pattern. Use the terms from Part | to answer each question. I 1I.-'l.|'hat is a proof? (1 point) I You want to prove a theorem in a twooolumn proof. You start with your given statement and list deductions in the left-hand column. What are the three main types of reasoning you will use for reasons in the right-hand column? [3 points; 1 point sum) 1 . Part II: Use the solution you found for x in Part I to find AB, BC, and AC. Show your work. (3 points) 3. Use the figure below to identify angles and segment lengths. 60 N M C D K H A JPPart I: Find the measure of _FED and the measure of ZDEN . Give an explanation for each angle in your answer. (1 point) Part II: Suppose the length of AD is 10 and the length of DG is twice as long as AD. Find the length of AG. Show your work. (1 point)Part III: Name a pair of vertical angles, a straight angle, and two acute angles other than ZGEN . (1 point) Part IV: Describe the term linear pair, and give an example from the diagram above. (1 point)4. A pair of lines may be parallel. perpendiculan pr skew. Part I: Describe parallel lines and include a sketch that shows parallel lines. Give a realworld example of parallel lines. Use apprcpriate labeling and symbols. (2 [Wilma] Part II: Describe perpendicular lines and include a sketch that shows perpendicular lines. Give a realworld example of perpendicular lines. Use appropriate labeling and symbols. (2 paints) Part III: Describe skew lines and include a sketch that shows skew lines. Give a real-world example of skew lines. Use appropriate labeling and symbols. (2 points) 5. A C n/m D E H6. Look at the sequence below and form a conjecture (educated guess) about it. Part I: This form of reasoning, where you form general ideas and rules based on your experiences and observations, is called (1 point) Part II: Describe the pattern of the following sequence. (2 points) Part III: Draw the next item in the series. (1 point)3". You just hung a picture twelve inches above the wall trim. Your friend thinks the picture looks crooked. Use what you know about parallel lines and transversals to determine if the picture is level. Step 1: You don't have a level, but you are in luck. You know the wall trim is level. You have a protractor and the sun is casting a shadow on the wall. Describe how you can determine if the picture is level. [3 points) Step 2: Assume you measured L3 and 45 and found them to be equal. Use the spaces provided below to complete a formal proofthat demonstrates the picture is level with the trim. {4 palm} I! I Partl: E II {E and g H 6H. Use the gure above to nd the values of each angle. Give an explanation for each angle value. (7 points) 6. Look at the sequence belovv and form a conjecture {educated guess} about it. Part I: This form of reasoning. where you form general ideas and rules based on your experiences and observations. is called . [1 point} Part II: Describe the pattern of the following sequence. {2 points) S picture 3 2 8 5 t wall trim 6 edge of Given: S,f, and t and m/3 = m45 shadow Prove: f t Statement Reason 1. 1. Given 2. 23 = 25 2. 3. 3. Vertical angles theorem 4. 13 = 27 4. Transitive property 5. 5. Corresponding angles theorem