3.14 Unit Test: Congruence and Constructions - Part 1

Question

12.1 and 2.23.1 and 3.2456789101112

satis · Answer

Alison should do for her first step :
  1.Points P is on the perpendicular
  1.KM is the bisector of ∠JKM                               Given
  m∠JNM = m∠KNL....................................Opposite angles
  △ABC = △JKL.............................................Congruent
  
Place the point of the compass on point M and draw an arc using width for the opening of the compass that is greater than ½ MN
  
 
  
     Bisector of AB                                                     Given
  
2. AX ≅ BX                                                              Definition of bisector
  
3. ∠PXA and ∠PXB are right angles                  Definition of perpendicular
  
4.ASA Congruence Postulate                            All right angles are congruent
  
5.PX ≅PX                                                                  Reflexive property of congruence
  
6. △AXP ≅△BXP                                                   SAS Congruency Postulate
  
7.PA ≅ PB                                                                Corresponding parts of   
                                                                                    congruent triangles are   
                                                                                    congruent
  
8.Point P is equidistance from                            Definition of equidistance
  
   Endpoints of AB   
 
  
2. ∠JKM =∠LKM                                                    Definition of bisector
  
3. ∠KXM and ∠KYM are right angles                Given
  
4. ∠KXM ≅ ∠KYM                                               All right angles are congruent
  
5.MK = MK                                                                          Reflexive Property of   
                                                                                    congruence
  
6. △KXM ≅△KYM                                                   AAS Congruence Postulate
  
7. MX ≅MY                                                              Corresponding parts of congruent triangles are congruent
  
8.Point P is equidistance from the                    Definition of equidistance
  
    sides of ∠JKL
  
.   
4x+6 = 7x-21
  
7x-4x = 6+21
  
3x = 27
  
x = 27/3 = 9
  
 m∠JNM = 4x + 6 = 4*9 + 6 = 42o
  
 
  
m∠A = m∠J ,  m∠B= m∠K, and m∠C = m∠L
  
So, m∠K = m∠B = 55o
  
m∠L = 25o
  
In △JKL :
  
m∠J = 180o –( m∠K + m∠L) = 180o –(  55o + 25o)= 100o

Tusharroul · Answer

Options are missing in question number 10.

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3.14 Unit Test: Congruence and Constructions - Part 1

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