Select ,begin emphasis,all,end emphasis, of the diagrams that contain enough information to determine that triangle Q R S is isosceles.
Answer options with 6 options
A.
A diagram.Short description, A diagram.,Long description,
The diagram shows triangle Q R S on line P T. In order from left to right, the points on the line are P, Q, S, T. Point R, the apex of triangle Q R S, is above the line, between points Q and S. The exterior angle P Q R is labeled 100°. The interior angle Q R S is labeled 80°. No other angles are labeled.
B.
A diagram.Short description, A diagram.,Long description,
The diagram shows triangle Q R S on line P T. In order from left to right, the points on the line are P, Q, S, T. Point R, the apex of triangle Q R S, is above the line, between points Q and S. The exterior angle P Q R is labeled 100°. The interior angle R S Q is labeled 80°. No other angles are labeled.
C.
A diagram.Short description, A diagram.,Long description,
The diagram shows triangle Q R S on line P T. In order from left to right, the points on the line are P, Q, S, T. Point R, the apex of triangle Q R S, is above the line, between points Q and S. The exterior angle P Q R is labeled 100°. The interior angle R S Q is labeled 40°. No other angles are labeled.
D.
A diagram.Short description, A diagram.,Long description,
The diagram shows triangle Q R S on line P T. In order from left to right, the points on the line are P, Q, S, T. Point R, the apex of triangle Q R S, is above the line, between points Q and S. The exterior angle P Q R is labeled 100°. The interior angle Q R S is labeled 40°. No other angles are labeled.
E.
A diagram.Short description, A diagram.,Long description,
The diagram shows triangle Q R S on line P T. In order from left to right, the points on the line are P, Q, S, T. Point R, the apex of triangle Q R S, is above the line, between points Q and S. The interior angle Q R S is labeled 40°. The interior angle R S Q is labeled 80°. No other angles are labeled.
F.
A diagram.Short description, A diagram.,Long description,
The diagram shows triangle Q R S on line P T. In order from left to right, the points on the line are P, Q, S, T. Point R, the apex of triangle Q R S, is above the line, between points Q and S. The exterior angle P Q R is labeled 100°. The exterior angle R S T is labeled 100°. No other angles are labeled.
1 answer
To determine whether triangle QRS is isosceles, we need to identify cases where two angles are equal or two sides are determined to be equal through the angles.
After analyzing the options provided:
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Option A: The angles do not provide enough information to conclude that QRS is isosceles.
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Option B: The angle QRS (80°) and the angle RQS were given, which allows for the possibility of concluding that triangle QRS is isosceles if RQS is also 80°. However, it does not adequately support isosceles definitively as only one angle is specified.
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Option C: With an angle RQS given as 40°, and the exterior angle PQR being 100°, this leads to the conclusion that angle QRS = 100 - 40 = 60°. This is not sufficient for an isosceles triangle as there are no equal angles.
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Option D: Given angle QRS = 40° and PQR = 100°, it doesn’t imply any two sides will be equal.
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Option E: With angles QRS=40° and RQS=80°, we have different angles again. This does not support the isosceles triangle definition.
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Option F: Two exterior angles are both 100°, while we don’t know the internal angles completely, the concept of two equal exterior angles would imply congruence in the opposing angles, inferring that the two angles would likely confirm isosceles status.
From this analysis, only Option F stands out suggesting the triangle QRS can be inferred to be isosceles due to potential equality in angles derivatively.
Answer: F.
