Section 1-4 - Parallel Lines And Angles-KEY

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Sec 1.4 CC Geometry – Parallel Lines and AnglesName:PARALLEL LINESG EXTERIOR1A B 32 4CThese symbolsimply the twolines are parallel.INTERIOR5 D7 EXTERIOR6 E 8HWORD BANK: Consecutive Interior Angles Alternate Interior AnglesTransversal F Congruent Vertical AnglesAlternate Exterior AnglesCorresponding AnglesConsecutive Exterior AnglesSupplementary 1. Give an alternate name for angle using 3 points:(1 answer)2. Angles (2 answers)and 3. Angles and can best be described as:can best be described as:(2 answers)4. The line ⃖ ⃗ can best be described as a:(1 answer)5. Which angle corresponds to (1 answer)6. Angles and 7. Angles and :can best be described as:can best be described as:8. Which angle is an alternate interior angle with 9. Angles and 10. Angles and (2 answers)(2 answers):can best be described as:(2 answers)can best be described as:11. Which angle is an alternate exterior angle with 12. Which angle is a vertical angle to (2 answers)::13. Which angle can be described as consecutive exterior angle with :14. Any two angles that sum to 180 ̊ can be described asM. Winking (Section 1-4)(1 answer)(1 answer)(1 answer)(1 answer)angles. (1 answer)p.17

TRIANGLE’s INTERIOR ANGLE SUM1. a. First, Create a random triangle on a piece of pattypapers.b. Using your pencil, write a number inside each interior angle alabel.2312c.d.Next, cut out the triangle.31Finally, tear off or cut each of the angles fromthe trianglee. Using tape, carefully put all 3 angles next to one another so thatthey all have the same vertex and the edges are touching but theyaren’t overlappingPaste or Tape your 3 vertices here: Common Vertex2. What is the measure of a straight angle or the angle that creates a line by using twoopposite rays from a common vertex?3. Collectively does the sum of your 3 interior angles of a triangle form a straight angle?What about others in your class?4. Make a conjecture about the sum of the interior angles of a triangle. Do you think yourconjecture will always be true? (please explain using complete sentences)M. Winking (Section 1-4)p.18

5. More formally, why do the 3 interior angles of any triangle sum to 180 ̊ ?Consider ABC. The segmentis extended into a line and a parallel line is constructed⃖⃗ ⃖ ⃗.through the opposite vertex. So,a. Why is ?b. Why is ?c. Why is ?d. Using substitution we can replace with andinterior angles of a triangle must always sum to 180̊.() ( with) to show that the Write the angle number in theand then write the letter that corresponds with the numberbased on the code at the bottom in the box.7. Angle 2 and Angleare alternate exterior angles.8. Angle 7 and Angleare alternate exterior angles.9. Angle 4 and Angleare corresponding angles.10. Angle 5 and Angleare consecutive interior angles.11. Angle 3 and Angleare alternate interior angles.12. Angle 7 and Angleare consecutive exterior angles.13. Angle 6 and Angleare vertical angles.14. Angle 2 and Angleare a linear pair and on the same side of the transversal.15. Angle 1 and Angleare corresponding angles.1 D2 U3 L4 A5 N1 23 46 I5 67 87 E8 CWhat type of Geometry is this?M. Winking (Section 1-4)p.19

16. Given lines p and q are parallel, find the value of x that makes each diagram true.a.b.(6x 5)ºqq(6x 5)º(2x 45)º(2x 15)ºppx x 17. Given lines m and n are parallel, find the value y of that makes each diagramtrue.a.40ºb.mm130ºnyºn130ºyº40ºy y 18. ANGLE PUZZLE. Find AEFGiven: m DEF 85 m ABG 50 BAE is a right angle CGE and DEG are supplementaryC BD G E Am AEF F M. Winking (Section 1-4)p.20

19. Converse of AIA, AEA, CIA, CEA.CEA Which sets of lines are parallel and explain why?a.b.70º80ºqqpp120º50º20. By which property (SSS, AA, SAS) are the triangles similar ( RSQ UST)?)? Explain why.What is the measure of TU?1021. Using (SSS, AA, SAS) which triangles can you determine must be similar? (explain why)A)B)C)circle onecircle oneSimilar?SSSYESAANOSASD)Similar?SSSYESAAcircle oneNOSimilar?SASSSSYESAANOSASE)circle onecircle oneSimilar?SSSYESAASimilar?NOSSSSASM. Winking (Section 1-4)YESAANOSASp.21

22. Using some type of similar figure find the unknown lengths.A.B.xC.x3 cm565 cm6 cm1222a.x 22b.x C.22c.y D.6 cm8 cmx10 cmHINT:22c.x 22d.x M. Winking (Section 1-4)p.22

Prove the Pythagorean Theorem (a2 b2 c2) using similar right triangles:M. Winking (Section 1-4)p.23

Sec 1.4 CC Geometry – Parallel Lines and Angles Name: PARALLEL LINES 1. Give an alternate name for angle Û using 3 points: (1 answer) 2. Angles m n q and o n s can best be described as: (2 answers) 3. Angles ß and Ü can best be described as: (2 answers) 4. The line

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