Nae Date. Congruence and Transforations For use with Eploration. Essential Question What conjectures can ou ae about a figure reflected in two lines? 1 EXLORTION: Reflections in arallel Lines Go to igideasmath.co for an interactive tool to investigate this eploration. Wor with a partner. se dnaic geoetr software to draw an scalene triangle and label it C. a. Draw an line DE. Reflect C in DE to for C. b. Draw a line parallel to DE. Reflect C in the new line to for C. c. Draw the line through point that is perpendicular to DE. What do ou notice? d. Find the distance between points and. Find the distance between the two parallel lines. What do ou notice? e. Hide ' C ' '. Is there a single transforation that aps C to C. Eplain. f. Mae conjectures based on our answers in parts (c) (e). Test our conjectures b changing C and the parallel lines. Copright ig Ideas Learning, LLC Geoetr 107
Nae Date. Congruence and Transforations (continued) EXLORTION: Reflections in Intersecting Lines Go to igideasmath.co for an interactive tool to investigate this eploration. Wor with a partner. se dnaic geoetr software to draw an scalene triangle and label it C. a. Draw an line DE. Reflect C in DE to for C. b. Draw an line DF so that EDF is less than or equal to 90. Reflect C in DF to for C. c. Find the easure of EDF. Rotate C counterclocwise about point D twice using the easure of EDF. d. Mae a conjecture about a figure reflected in two intersecting lines. Test our conjecture b changing C and the lines. Counicate Your nswer 3. What conjectures can ou ae about a figure reflected in two lines?. oint Q is reflected in two parallel lines, GH and JK, to for Q and Q. The distance fro GH to JK is 3. inches. What is the distance QQ? 108 Geoetr Copright ig Ideas Learning, LLC
Nae Date. Notetaing with Vocabular For use after Lesson. In our own words, write the eaning of each vocabular ter. congruent figures congruence transforation Theores Theore. Reflections in arallel Lines Theore If lines and are parallel, then a reflection in line followed b a reflection in line is the sae as a translation. If is the iage of, then 1. is perpendicular to and, and. = d, where d is the distance between and. d roof E. 31. p. 06 Notes: Theore.3 Reflections in Intersecting Lines Theore If lines and intersect at point, then a reflection in line followed b a reflection in line is the sae as a rotation about point. The angle of rotation is, where is the easure of the acute or right angle fored b lines and. roof E. 31. p. 06 Notes: Copright ig Ideas Learning, LLC Geoetr 109
Nae Date. Notetaing with Vocabular (continued) Etra ractice 1. Identif an congruent figures in the coordinate plane. Eplain. E H K F G L Q M J O D R C V N T S. Describe a congruence transforation that aps QR to ST. T S Q R 3. Describe a congruence transforation that aps polgon CD to polgon EFGH. C F D G E H 110 Geoetr Copright ig Ideas Learning, LLC
Nae Date. Notetaing with Vocabular (continued) In Eercises and 5, deterine whether the polgons with the given vertices are congruent. se transforations to eplain our reasoning.. (, ), ( 3, 1 ), C( 1, 1 ) and D(, ), E( 3, 1 ), F( 1, 1) 5. G( 3, 3 ), H(, 1 ), I( 6, ), J( 6, 3 ) and K(, 1 ), L( 3, 3 ), M(, ), N(, 1) In Eercises 6 9,, V is reflected in line, and V is reflected in line. 6. translation aps V onto which segent? 7. Which lines are perpendicular to? V V V 8. Wh is V the iage of V? Eplain our reasoning. 9. If the distance between and is 5 inches, what is the length of VV? 10. What is the angle of rotation that aps onto? 60 Copright ig Ideas Learning, LLC Geoetr 111