Triangle QSR: Angle Q is 98 degrees, and angle R is 37.6 degrees.
Triangle TUV: Angle U is 98 degrees, and angle V is 37.6 degrees.

Which statement is not true about these triangles?

A. ∠Q ≅ ∠T based on the third angle theorem.
B. ∠S corresponds to ∠V.
C. ∆QRS ~ ∆TVU based on the angle-angle criterion.
D. ∆RQS ~ ∆VTU based on the angle-angle criterion.

Question

High School

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Answer :

ConnorRobert ConnorRobert · Answer 1 · 2024-12-05T06:37:42-05:00

The statement "∠S corresponds to ∠V" is not true about these triangles.

1. ∠Q ≅ ∠T based on the third angle theorem:

The third angle theorem states that in any triangle, if two angles are congruent, then the third angle must also be congruent. Since ∠Q = 98 degrees and ∠T = 98 degrees, by the third angle theorem, ∠Q ≅ ∠T. Therefore, this statement is true.

2. ∠S corresponds to ∠V:

Corresponding angles in similar triangles are congruent. However, to determine if ∠S corresponds to ∠V, we need to establish that the triangles are similar. We cannot directly conclude this based on the given information because having two angles congruent in two triangles does not guarantee similarity. So, this statement is not necessarily true.

3. ∆QRS ~ ∆TVU based on the angle-angle criterion:

If two triangles have two pairs of corresponding angles that are congruent, then the triangles are similar. Here, ∠Q ≅ ∠T and ∠R ≅ ∠V, so by the angle-angle criterion, ∆QRS ~ ∆TVU. Therefore, this statement is true.

4. ∆RQS ~ ∆VTU based on the angle-angle criterion:

Similar to the previous statement, ∆RQS ~ ∆VTU based on the angle-angle criterion because ∠Q ≅ ∠T and ∠S ≅ ∠U. Therefore, this statement is true.