Sec 1.4 CC Geometry Parallel Lines and Angles Name:
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1 PARALLEL LINES Sec 1.4 CC Geometry Parallel Lines and Angles Name: A D EXTERIOR INTERIOR 5 6 E 7 8 G 1 2 B 3 4 C F These symbols imly the two lines are arallel. EXTERIOR H WORD BANK: Alternate Interior Angles DEH HEF Corresonding Angles Sulementary GBC Consecutive Interior Angles 5 Transversal Congruent 4 Vertical Angles Alternate Exterior Angles Consecutive Exterior Angles ABG 1. Give an alternate name for angle 2 using 3 oints: (1 answer) 2. Angles ABE and CBG can best be described as: (2 answers) 3. Angles 6 and 3 can best be described as: (2 answers) 4. The line GH can best be described as a: (1 answer) 5. Which angle corresonds to DEB : (1 answer) 6. Angles FEB and CBE can best be described as: (2 answers) 7. Angles 1 and 8 can best be described as: (2 answers) 8. Which angle is an alternate interior angle with CBE : (1 answer) 9. Angles GBC and BEF can best be described as: (2 answers) 10. Angles 2 and 8 can best be described as: (2 answers) 11. Which angle is an alternate exterior angle with ABG : (1 answer) 12. Which angle is a vertical angle to ABG : (1 answer) 13. Which angle can be described as consecutive exterior angle with 1 : (1 answer) 14. Any two angles that sum to 180 can be described as angles. (1 answer).17
2 TRIANGLE s INTERIOR ANGLE SUM 1. a. First, Create a random triangle on a iece of atty aers. b. Using your encil, write a number inside each interior angle a label c. Next, cut out the triangle d. Finally, tear off or cut each of the angles from the triangle e. Using tae, carefully ut all 3 angles next to one another so that they all have the same vertex and the edges are touching but they aren t overlaing Paste or Tae your 3 vertices here: Common Vertex 2. What is the measure of a straight angle or the angle that creates a line by using two oosite 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 your conjecture will always be true? (lease exlain using comlete sentences).18
3 5. More formally, why do the 3 interior angles of any triangle sum to 180? Consider ABC. The segment AB is extended into a line and a arallel line is constructed through the oosite vertex. So, AB CD. a. Why is 1 2? b. Why is 5 4? c. Why is m 2 + m 3 + m 4 = 180? d. Using substitution we can relace m 2 with m 1 and m 4 with m 5 to show that the interior angles of a triangle must always sum to 180. ( ) + m 3 + ( ) = 180 Write the angle number in the and then write the letter that corresonds with the number based on the code at the bottom in the box. 7. Angle 2 and Angle are alternate exterior angles. 8. Angle 7 and Angle are alternate exterior angles. 9. Angle 4 and Angle are corresonding angles. 10. Angle 5 and Angle are consecutive interior angles. 11. Angle 3 and Angle are alternate interior angles. 12. Angle 7 and Angle are consecutive exterior angles. 13. Angle 6 and Angle are vertical angles. 14. Angle 2 and Angle are a linear air and on the same side of the transversal. 15. Angle 1 and Angle are corresonding angles. 1=D 2=U 3= L 4 = A 5 = N 6 = I 7 = E 8 = C What tye of Geometry is this?.19
4 16. Given lines and are arallel, find the value of x that makes each diagram true. a. b. (6x+5)º (6x+5)º (2x+45)º (2x+15)º 17. Given lines m and n are arallel, find the value y of that makes each diagram true. a. b. m 130º n 40º m 40º yº 130º yº n y = y = 18. ANGLE PUZZLE. Find AEF Given: m DEF 85 m ABG 50 BAE is a right angle CGE and DEG are sulementary B G C D m AEF A E F.20
5 19. Converse of AIA, AEA, CIA, CEA. Which sets of lines are arallel and exlain why? a. 70º b. 80º 120º 50º 20. By which roerty (SSS, AA, SAS) are the triangles similar ( RSQ~ UST)? Exlain why. 10 What is the measure of TU? 21. Using (SSS, AA, SAS) which triangles can you determine must be similar? (exlain why) A) B) C) D) E) Similar? SSS YES NO AAA SAS.21
6 22. Using some tye of similar figure find the unknown lengths. A. x B. C. 3 cm x cm 6 cm 12 22a. 22b. 22c. y = C. 6 cm D. 8 cm x 10 cm HINT: 22c. 22d..22
7 Prove the Pythagorean Theorem (a 2 + b 2 = c 2 ) using similar right triangles:.23
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