Chapter 3 Test Review Question Answers. Since AC > BC, 3x + 6 > 4x - 5. x < < x < 11. 2x - 3 = x + 10 P = 2( 13) ( 13) - 5
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1 1. In right, find all the restrictions on the value of x. 3x + 6 ince >, 3x + 6 > 4x - 5 4x - 5 > 0 x < 11 x > 5 4 4x < x < 11. Find all possible values for the perimeter of isosceles ZO. O 1st possibility is that OZ O: x - 3 x + 10 x - 3 = x + 10 x = 13 P = ( 13) ( 13) - 5 Z 3x - 5 = 80 nd possibility is that OZ Z: x - 3 = 3x - 5 x = ides are 1, 1, and 1, which is not a triangle!! 3rd possibility is that Z O: 3x - 5 = x + 10 x = 15 ( 15 ) = ( ) - 5 o, the perimeter can be 80 or 47. aroody Page 1 of 6
2 34 +x m > m Find the restrictions on the value of x 15 - x ince >, 34 + x > 15 - x x > x > 0 x < < x < 15 HN is isosceles with base N. Points & Y are midpoints of HN & H, respectively. HN = 8x - 6; Y = 3x + 6; N = 4x. Find P, the perimeter of HN. H 8x - 6 = ( 3x + 6) x = 18 Y x = 9 P = ( 8( 9) - 6) + 4( 9) = ( 66) + 36 = 168 N aroody Page of 6
3 is isosceles easons 1... Given eflexive Property ( 1,, 3) PT onverse of ITT 7. is isosceles 7. efinition of Isosceles 6. PO P 1 1 P JPN is isosceles J O easons N PO P. Given PO PO ITT JO & ON are straight s ssumed from diagram PO is supp. to POJ If s form a straight, they are supp. 6. PO is supp. to PN 6. ame as 5 7. JOP NP 7. upps. of s are 8. JOP NP 8. ( 1,, 7) 9. JP NP 9. PT 10. JPN is isosceles 10. efinition of Isosceles aroody Page 3 of 6
4 7. F NK 1 4 F 1 N 3 4 K I easons I. ll radii of a are F K ame as F NK Given N ubtraction Property of egments 6. NI 6. VT 7. NI 7. (, 6, 5) PT 9. F & KN are straight s 9. ssumed from diagram is supp to 10. If s form a straight, they are supplementary is supp to ame as upplements of s are & are altitudes is isosceles easons L H 1. & are altitudes. ;. efinition of altitude & are right s efinition of Given eflexive Property is isosceles Given HL ( 3, 5, 4) PT 8. onverse of ITT 9. efinition of Isosceles aroody Page 4 of 6
5 9. M ML; P LP M P & I are midpoints L LI M L I P easons 10. H L 1. M ML; P LP. M & P are right s raw L L L M P 6. ML PL 7. ML LP 8. & I are midpoints 9. L LI. efinition of egments uxiliary Lines eflexive Property Given 6. HL (, 4, 5) 7. PT 8. Given 9. ivision Property of egments easons 1... Given & are right s efinition of egments T 1 Given ubtraction Property of s eflexive Property ( 4, 7, 6) PT aroody Page 5 of 6
6 F is isosceles 1 3 F easons Given onverse of ITT eflexive Property ( 1, 4, 3) PT 7. F F 7. ubtraction Property of s 8. F F 8. onverse of ITT 9. F is isosceles 9. efinition of isosceles U Y TU is an altitude to Y is an altitude to T T is isosceles U Y T eflexive Property. U Y. Given TU is an altitude to Given Y is an altitude to T Given TU ; Y T efn. of ltitude of a 6. UT & Y are right s 7. UT Y efn. of segments T 8. Y UT 8. ( 1,, 7) 9. T 10. T T 11. U TY 1. T T 1 T 1 T is isosceles easons 9. PT 10. ITT 11. PT 1. ubtraction Property of s 1 onverse of ITT 1 efinition of Isosceles aroody Page 6 of 6
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