Triangles A B C and R M Q are shown. Angles C A B and M R Q are 29 degrees. Angles A B C and R M Q are 116 degrees. What additio
nal information could be used to prove that the triangles are congruent using AAS? Select two options
2 answers:
Answer:
Therefore, the two options for triangles to be congruent using AAS are
1. BC ≅ MQ (Additional information)
2. AC ≅ RQ (Additional information)
Step-by-step explanation:
Given:
∠CAB =∠MRQ = 29°
∠ABC = ∠RMQ = 116°
To Prove:
Δ ABC ≅ ΔRMQ by AAS congruence test which additional information is required
Proof:
<u>Case 1.</u>
In Δ ABC and Δ RMQ
∠CAB =∠MRQ = 29° ……….{Given}
∠ABC = ∠RMQ = 116° ..……..{Given}
BC ≅ MQ ……….{Additional information required}
Δ ABC ≅ Δ RMQ ….{By Angle-Angle-Side congruence test}
<u>Case 2.</u>
In Δ ABC and Δ RMQ
∠CAB =∠MRQ = 29° ……….{Given}
∠ABC = ∠RMQ = 116° ..……..{Given}
AC ≅ RQ ……….{Additional information required}
Δ ABC ≅ Δ RMQ ….{By Angle-Angle-Side congruence test}
Therefore, the two options for triangles to be congruent using AAS are
1. BC ≅ MQ (Additional information)
2. AC ≅ RQ (Additional information)
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y>14/2=7
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3. Remark, check the figures:
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In picture 1 wee see that the side lengths can be as large as we want. We can erect an altitude, as high as we want. Pick a point on the altitude, and join it to the endpoints of the base, and we get an isosceles triangle with base equal to 14.
2. According to the "triangle inequality" :
y+y>14
2y>14
y>14/2=7
(y is greater than 7)
3. Remark, check the figures:
the side lengths cannot be less than (neither equal to 7), because we cannot get a triangle in that case, check picture 2
In picture 1 wee see that the side lengths can be as large as we want. We can erect an altitude, as high as we want. Pick a point on the altitude, and join it to the endpoints of the base, and we get an isosceles triangle with base equal to 14.