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Name_____________________________________ Class____________________________ Date________________ Lesson 1-7 Lesson Objectives 1 Use a compass and a straightedge to construct congruent segments and congruent angles 2 Use a compass and a straightedge to bisect segments and angles Basic Constructions NAEP 2005 Strand: Geometry Topic: Relationships Among Geometric Figures Local Standards: ____________________________________ Vocabulary. A straightedge is A compass is Perpendicular lines are A perpendicular bisector of a segment is An angle bisector is A D C B J K N L Examples. 1 Constructing Congruent Segments Construct TW congruent K to KM. Step 1 Draw a ray with endpoint T. M T Step 2 Open the compass the length of KM. Step 3 With the same compass setting, put the compass point on point T. Draw an arc that intersects the ray. Label the point of intersection W. T W KM TW 24 Geometry Lesson 1-7 Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved. Construction is Name_____________________________________ Class____________________________ Date ________________ 2 Constructing Congruent Angles Construct Y so that Y G. Step 1 Draw a ray with endpoint Y. Y G 75 All rights reserved. Step 2 With the compass point on point G, draw an arc that intersects both sides of G. Label the points of intersection E and F. E G 75 F © Pearson Education, Inc., publishing as Pearson Prentice Hall. Step 3 With the same compass setting, put the compass point on point Y. Draw an arc that intersects the ray. Label the point of intersection Z. Y Step 4 Open the compass to the length EF. Keeping the same compass setting, put the compass point on Z. Draw an arc that intersects with the arc you drew in Step 3. Label the point of intersection X. Y ) Step 5 Draw YX to complete Y. Y G Daily Notetaking Guide Z X Y Z Geometry Lesson 1-7 25 Name_____________________________________ Class____________________________ Date ________________ 3 Constructing the Perpendicular Bisector Given: AB. * ) * ) Construct: XY so that XY AB at the midpoint M of AB. A B A B A B Step 2 With the compass setting, put the compass point on point B and draw another long arc. Label the points where the two arcs as X and Y. * ) Step 3 Draw XY . The point of intersection of AB and XY is M, the of AB. * ) X * ) A XY AB at the midpoint of AB, so XY is the of AB. * B Y ) 4 Finding Angle Measures WR bisects AWB so that mAWR x A and mBWR 4x 48. Find mAWB. R x W m m Definition of Substitute for mAWR and for mBWR. 48 Subtract x from each side. Divide each side by mAWR Substitute ( ) mBWR 4 mAWB m mAWB 26 4x 48 B Geometry Lesson 1-7 for x. 48 m . Postulate Substitute for mAWR and for mBWR. Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. * ) All rights reserved. Step 1 Put the compass point on point A and draw a long arc. Be sure that the opening is than 12AB. Name_____________________________________ Class____________________________ Date ________________ Quick Check. 1. Use a straightedge to draw XY. Then construct RS so that RS 2XY. All rights reserved. 2. a. Construct F with mF 2mB. B ) b. Explain how you can use your protractor to check that YP is the angle bisector of XYZ. © Pearson Education, Inc., publishing as Pearson Prentice Hall. X P Y Z 3. Draw ST. Construct its perpendicular bisector. ) 4. If mJKN 50°, then find mNKL and mJKL. KN bisects JKL. J K N Daily Notetaking Guide mNKL , mJKL L Geometry Lesson 1-7 27