Practice B 3-4 Perpendicular Lines - PBworks

1 Copyright by Holt, Rinehart and Winston. 28 Holt GeometryAll rights Date ClassLESSONP ractice BPerpendicular Lines3-4 For Exercises 1 4, name the shortest segment from the point to the line and write an inequality for x. (Hint: One answer is a double inequality.) 1. 2. 11'()*X 4 _ PR ; x _ HJ ; x 7 3. 6"#$!X 3 4. 2134576X 4X _ AB ; x 9 _ UT ; x 17 Complete the two-column proof.

2 5. Given: m n Prove: 1 and 2 are a linear pair of congruent angles. Proof:StatementsReasons1. a. m n1. Given2. b. m 1 90 , m 2 90 2. Def. of 3. 1 23. c. Def. of 4. m 1 m 2 180 4. Add. Prop. of 5. d. 1 and 2 are a linear Def. of linear pair 6. The Four Corners National Monument is at the intersection of the borders of Arizona, Colorado, New Mexico, and Utah. It is called the four corners because the intersecting borders are Perpendicular . If you were to lie down on the intersection, you could be in four states at the same time the only place in the United States where this is possible.

3 The figure shows the Colorado-Utah border extending north in a straight line until it intersects the Wyoming border at a right angle. Explain why the Colorado-Wyoming border must be parallel to the Colorado New Mexico border. Possible answer: All the borders are straight Lines , and the Colorado Utah border is a transversal to the Colorado Wyoming and the Colorado New Mexico borders. Because the transversal is Perpendicular to both borders, the borders must be by Holt, Rinehart and Winston. 57 Holt GeometryAll rights by Holt, Rinehart and GeometryAll rights Date ClassLESSON3-4 Practice APerpendicular Lines 1.

4 The Perpendicular bisector of a segment is a line perpendicularto a segment at the segment s midpoint. 2. The shortest segment from a point to a line is Perpendicular to the line . For Exercises 3 and 4, name the shortest segment from the point to the line and write an inequality for x. _AB;x 23 _FE;x 8 Fill in the blanks to complete these theorems about parallel and Perpendicular Lines . 5. If two coplanar Lines are Perpendicular to the same line , then the two Lines are parallel to each other. 6. If two intersecting Lines form a linear pair of congruent angles, then the Lines are Perpendicular .

5 7. In a plane, if a transversal is Perpendicular to one of two parallel Lines , then it is Perpendicular to the other the drawing of a basketball goal for Exercises 8 10. In each exercise, justify Esperanza s conclusion with one of the completed theorems from Exercises 5 7. Write the number 5, 6, or 7 in each blank to tell which theorem you used. 8. Esperanza knows that the basketball pole intersects the court to form a linear pair of angles that are congruent. She concludes that the pole and the court are Perpendicular . 6 9. Esperanza knows that the hoop and the court are both Perpendicular to the pole.

6 She concludes that the hoop and the court are parallel to each other. 5 10. Esperanza knows that the hoop and the court are parallel to each other. She also knows that the hoop is Perpendicular to the pole. Esperanza concludes that the pole and the court are Perpendicular . 7polehoopcourtCopyright by Holt, Rinehart and GeometryAll rights Date ClassLESSONP ractice BPerpendicular Lines3-4 For Exercises 1 4, name the shortest segment from the point to the line and write an inequality for x. (Hint: One answer is a double inequality.) 4_PR;x _HJ ;x 7 4 _AB;x 9 _UT;x 17 Complete the two-column proof.

7 :m nProve: 1 and 2 are a linear pair of congruent n1. 1 90 , m 2 90 2. Def. of 3. 1 23. of 4. m 1 m 2 180 4. Add. Prop. of 1 and 2 are a linear Def. of linear pair 6. The Four Corners National Monument is at the intersection of the borders of Arizona, Colorado, New Mexico, and Utah. It is called the four corners becausethe intersecting borders are Perpendicular . If you were to lie down on the intersection, you could be in four states at the same time the only place in the United States where this is possible. The figure shows the Colorado-Utah border extending north in a straight line until it intersects the Wyoming border at a right angle.

8 Explain why the Colorado-Wyoming border must be parallel to the Colorado New Mexico border. Possible answer:All the borders are straight Lines , and the Colorado Utah border is a transversalto the Colorado Wyoming and the Colorado New Mexico borders. Because thetransversal is Perpendicular to both borders, the borders must be 2 NewMexicoArizonaColoradoWyomingUtahCopyr ight by Holt, Rinehart and GeometryAll rights Date ClassLESSON3-4 Practice CPerpendicular Lines 1. Draw a segment a little more than half the width of this page. Label this segment with length x, then use a compass and straightedge to construct a segment that has length5__4x.

9 1 2 1 4 5 4 2. Among segments _BA ,_BC,_BD, and_BE, which is the shortest segment in the figure? Name the second shortest segment. Explain your _BD must be shorter than _BE,x 11. Therefore _BC is the shortest segment. If x 1, then _BD would be the second shortest segment, but if x 3, then _AB would be the second shortest segment. So there is not enough information given in the figure to say which is the second shortest segment. 3. Use a straightedge to draw a triangle. Construct the Perpendicular bisector of each side of the triangle, and extend the bisectors into the interior of the triangle.

10 Mark the point of intersection of the three bisectors. This is the circumcenter of the triangle. Use your compass to compare the distance from the circumcenter to each vertex of the triangle. What is remarkable about the distances? The distances are equal. Now construct a circle completely around the triangle through all three vertices with your compass. You have circumscribed a circle around a triangle. 4. An architect designs a triangular jogging track around a circular pond. Each side of the track just touches the pond. The circle is inscribed in the triangle.