x=7

x=14

No Solution

x=5.5

T,T,T,T,T,T,T,T

F,F,F,F,F,F,F,F

T,F,T,F,T,F,T,F

T,T,F,F,T,T,F,F

33

58

29

11

\[1.) WY ≅ XV , VW ┴ WX , YX ┴ WX\] 1.) Given \[2.) ∠VWX ≅ ∠YXZ\] 2.) Definition of Perpendicular Lines \[3.) ∠VWX and ∠YXZ = right angles\] 3.) Right Angle Congruency\[4.) WX ≅ WX\] 4.) Reflexive Property \[5.) ΔXWY ≅ ΔWXY\] 5.) SAS congruency

\[1.) WY ≅ XV , VW ┴ WX , YX ┴ WX\] 1.) Given \[2.) ∠VWX ≅ ∠YXZ\] 2.) Right Angle Congruency \[3.) ∠VWX and ∠YXZ = right angles\] 3.) Definition of Perpendicular Lines \[4.) WX ≅ WX\] 4.) Reflexive Property \[5.) ΔXWY ≅ ΔWXY\] 5.) SAS congruency

\[1.) WY ≅ XV , VW ┴ WX , YX ┴ WX\] 1.)Given \[2.) ∠VWX and ∠YXZ = right angles\] 2.) Definition of Perpendicular Lines \[3.) ∠VWX ≅ ∠YXZ\] 3.) Right Angle Congruency \[4.) WX ≅ WX\] 4.) Reflexive Property \[5.) ΔXWY ≅ ΔWXY\] 5.) Hypotenuse Leg congruency

\[1.) WY ≅ XV , VW ┴ WX , YX ┴ WX\] 1.)Given \[2.) ∠VWX and ∠YXZ\] are right angles 2.) Right Angle Congruency \[3.) ∠VWX ≅ ∠YXZ\] 3.) Definition of Perpendicular Lines \[4.) WX ≅ WX\] 4.) Reflexive Property \[5.) ΔXWY ≅ ΔWXY\] 5.) AAS congruency

\[ABC, CBG, ADI, FGH\]

\[CBA, DAF, HGF\]

\[BAD, GFI, CBG, GFA\]

\[DAB, CBG, FAD\]

\[BC, AD, HI\]

\[AB, CD\]

\[AB, HI\]

\[AB, CD, HI\]

parallel; (m∠2) 78°≅ (m∠6) 78°

not parallel; (m∠2) 78° + (m∠6) 78° ≠ 180

parallel; (m∠2) 78° + (m∠6) 78° = 156°

not parallel; (m∠2) 78° + (m∠6) 78° ≠ 156°

alternate interior

alternate exterior

consecutive interior

corresponding

no angle pair

6.) = ASA congruency ... 7.) =CPCTC

6.) = SSS congruency ... 7.) =CPCTC

6.) = CPCTC ... 7.) =SAS congruency

6.) = SAS congruency ... 7.) =CPCTC

3rd = ΔHKI ≅ ΔHKJ (SSS concurrency), 4th = HI ≅ HJ (CPCTC)

3rd = IK ≅ KJ (Definition of midpoint), 4th = HI ≅ HJ (CPCTC)

3rd = HK ≅ HK (Reflexive Property), 4th = HI ≅ HJ (CPCTC)

3rd = IK ≅ KJ (Definition of midpoint), 4th = HK ≅ HK (Reflexive Property)

x = 32, y = 140

x = 140, y = 52

x = 52, y = 140

x = 38, y = 154

70°

80°

110°

140°

160°

5

3√5

3+√5

3√3

3√6

∠a, ∠b, ∠d

∠a, ∠c, ∠d

∠a, ∠c, ∠e

∠b, ∠c, ∠d

∠b, ∠c, ∠e

4.) = ST + LN = LN + NR (Segment Addition), 5.) = ST + LN [-LN] = LN [-LN] + NR (Subtraction)

4.) = ST + TU = LN + NR (Segment Addition), 5.) = ST = LN (Substitution)

4.) = ST + TU = LN + NR (Substitution), 5.) = ST + LN = LN + NR (Substitution)

4.) = ST + TU = LN + NR (Substitution), 5.) ST + TU = SU, LN + NR = LR (Segment Addition)

Isosceles

Right

Scalene

Equilateral