Respuesta :
Incomplete Question. The Complete Question with figure is below.
Answer:
Therefore, the Triangles ACB and RQM are Congruent by
- Angle -Side-Angle Congruence test.
- Angle-Angle-Side Congruence test.
Step-by-step explanation:
Given:
AB ≅ MR
∠CAB = 42°
∠MRQ = 42°
∠CBA = 53°
∠MQR = 85°
To Find:
Are the triangles congruent? Why or why not?
Solution:
Triangle sum property:
In a Triangle sum of the measures of all the angles of a triangle is 180°.
In ΔMRQ,
[tex]\angle MRQ+\angle MQR+\angle RMQ=180\°[/tex]
Substituting the values we get
[tex]42+85+\angle RMQ=180\\\angle RMQ=180-127=53\\\angle RMQ=53\°[/tex]
∠CBA ≅ ∠RMQ = 53° ...Transitive Property...... ( 1 )
Now,
In ΔACB and Δ RQM
∠CAB ≅∠MRQ = 42° ……….{Given}
AB ≅ MR ……….{Given}
∠CBA ≅ ∠RMQ = 53° ..……..{From ( 1 )}
ΔACB ≅ ΔRQM ......….{By Angle-Side-Angle Congruence test}
Also it can be Proved by A-A-S congruence test
In ΔACB,
[tex]\angle A+\angle B+\angle C=180\°[/tex]
Substituting the values we get
[tex]42+53+\angle C=180\\\angle C=180-95=85\\\angle ACB=85\°[/tex]
∠ACB ≅ ∠MQR= 85° ...Transitive Property...... ( 2 )
Now,
In ΔACB and Δ RQM
∠CAB ≅∠MRQ = 42° ……….{Given}
∠ACB ≅ ∠MQR= 85° .........{ From ( 2 ) }
AB ≅ MR ……….{Given}
ΔACB ≅ ΔRQM ......….{By Angle -Angle-Side Congruence test}
Therefore, the Triangles ACB and RQM are Congruent by
- Angle -Side-Angle Congruence test.
- Angle-Angle-Side Congruence test.
Answer:
B
Step-by-step explanation:
Yes, they are congruent by either ASA or AAS.
