EXERCISES Practice and Problem Solving

Transcription

1 XI ractice and roblem olving or more practice, see xtra ractice. ractice by xample xample (page 224) In each diagram, the red and blue triangles are congruent. Identify their common side or angle.. K X N Y Z eparate and redraw the indicated triangles. Identify any common angles or sides. 4. # and # 5. # and # 6. # and # 7. # and # 8. #JK and #K 9. # and # K X J xample 2 (page 225) 0. eveloping roof omplete the flow proof. iven: & > &, > rove: & > & a.? b.? d.? e.? c.? hapter 4 ongruent riangles

2 eveloping roof Name a pair of overlapping congruent triangles in each diagram. tate whether the triangles are congruent by,,,, or H.. iven: >, ', 2. iven: >, > ' N 3. iven: >, 4. iven: 6, 6, & > & > xamples 3, 4 (pages 225 and 226) eveloping roof lan a proof. s part of your plan, separate the overlapping triangles you use. 5. iven: > I, I >, 6. iven: ', ', &I and & are right '. > rove: > rove: > I pply Your kills 7. iven: & > &2, &3 > &4 8. iven: >, rove: # > # is the midpoint of. rove: # > # 3 4 pen-nded raw the diagram described raw a vertical segment on your paper. n the right side of the segment draw two triangles that share the given segment as a common side. 20. raw an angle. n your angle draw two triangles that have the given angle as a common angle. 2. raw two regular pentagons, each with its five diagonals. a. In one, shade two triangles that share a common angle. b. In the other, shade two triangles that share a common side. esson 4-7 sing orresponding arts of ongruent riangles

3 roof 22. raw two regular hexagons and their diagonals. or these diagrams, do parts (a) and (b) of the preceding exercise. Name a pair of overlapping congruent triangles in each diagram. tate whether the triangles are congruent by,,,, or H. lan and write a proof. 23. iven: 24. iven: >, Y ' YX, & > & ZX ' YX, X > ZY Z X Y lothes esign he figure at the right is part of a clothing design pattern. In the figure, n n, #, and #. 7 k is isosceles with base, and ml 56. H J 25. ind the measures of all the numbered angles in the figure. I >. Name two congruent triangles 2 3 and tell how you can prove them congruent. eveloping roof xercises 27 and 28 are proofs for xercises 5 and 6. opy and complete each proof. oes the proof match your plan? 27. iven: > I, I >, &I and & are right angles. rove: > I Need Help? In each of xercises 27 and 28, use twice. I a.? I I b.? I and are rt.. s g.? I h.? d.? e.? I I i.? j.? ostulate f.? heorem I c.? k.? hapter 4 ongruent riangles

4 28. iven: ', ', > rove: > tatements easons. ', ' a & and & are right angles. b # and # are right triangles. c > d. 9 e. 9 > 9 f. 9 roperty of ongruence 6. # > # g & > &, > h. 9 i. & > &9 j # > # k. 9 l. 9 > 9 m.9 roof ollow your plan for the given xercise and write a proof. 29. xercise xercise 8 hallenge 3. easoning raw a quadrilateral with 6 and 6, and its diagonals and intersecting at. abel your diagram to indicate the parallel sides. a. ist all the pairs of congruent segments that you can find in your diagram. b. riting xplain how you know that the segments you listed are congruent. roof rite a proof. 32. iven: >, > 33. iven: ', bisects, rove: & > & bisects &. rove: > esson 4-7 sing orresponding arts of ongruent riangles

5 tandardized est rep ultiple hoice hort esponse xtended esponse ake It to the N nline lesson quiz at eb ode: afa-0407 se the diagram at the right for xercises If m&kj = 25, what is m&kj? If m&kj = 30 and x = 7.4, what is the perimeter of #KJ? H. 4.8 I If m&jk = 47, what is m&j? he pentagon at the right is equilateral and equiangular. a. hat two triangles must be congruent to prove H > H? b. lan a proof to show H > H. 38. a. In the figure at the right, why is # > #? b. opy the figure. ark each angle that has measure x. c. hat is the value of x? xplain how you found your answer. d. hat is m&? e. hat is? xplain your answer. x J H 3 m 3 m x x K ixed eview esson omplete the plan for a proof. iven: & and & are right angles, >. rove: # > # lan: # and # are a. 9triangles with legs that are given to be b. 9. he hypotenuse is congruent to itself by the c. 9 roperty of ongruence. # > # by the d. 9 heorem. esson 3-7 esson 3-5 onstructions raw a line p and a point not on p. onstruct the described line. 40. line n through so that n ' p 4. line r through so that r 6 p rite an equation in point-slope form of the line that contains the given point and has the given slope. 42. (2, -6); slope (0, 5); slope 44. (-3, 6); slope (0, 0); slope 2 3 rite an equation in point-slope form of the line that contains the given points. 46. (, 4), (0, 2) 47. (3, -5), (6, 0) 48. X(-4, -3), Y(2, -8) hapter 4 ongruent riangles