Select ,begin emphasis,all,end emphasis, of the diagrams that contain enough information to determine that triangle Q R S is isosceles.

Question

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.

Answer 1

To determine if triangle QRS is isosceles, we need to identify cases where at least two angles are equal or any other information indicating equal sides.

Let's analyze the options:

A. The angles given (100° and 80°) do not allow us to conclude that QRS is isosceles, as neither angle is equal to the other.

B. The angles given are 100° and 80°, which also do not indicate that triangle QRS is isosceles.

C. The angles given are 100° and 40°. Since neither angle is equal, we cannot determine that triangle QRS is isosceles.

D. The angles given are 100° and 40° again. Neither of these angles is equal, so triangle QRS cannot be concluded as isosceles.

E. The angles given are 40° and 80°. These angles are not equal, so we cannot conclude that triangle QRS is isosceles.

None of the options provide enough information to determine that triangle QRS is isosceles based on the angles presented. All options result in a conclusion that triangle QRS is not isosceles.

Therefore, the selections that could hint at the triangle being isosceles do not exist in these options. So the answer would be none of the above contain enough information to determine that triangle QRS is isosceles.