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Question 5 of 10

In right triangle [tex]\( \triangle QRS \)[/tex], [tex]\( m\angle S = 73^\circ \)[/tex]. In right triangle [tex]\( \triangle TUV \)[/tex], [tex]\( m\angle V = 73^\circ \)[/tex]. Which similarity postulate or theorem proves that [tex]\( \triangle QRS \)[/tex] and [tex]\( \triangle TUV \)[/tex] are similar?

A. HL
B. AA
C. SSS
D. SAS

Sagot :

GinnyAnsweridn
To determine which similarity postulate or theorem proves that triangles Δ QRS and Δ TUV are similar, let's analyze the given information step-by-step:

1. Angle Information:

- In triangle Δ QRS, m∠ S = 73°.
- In triangle Δ TUV, m∠ V = 73°.

2. Similar Angle:

Both triangles Δ QRS and Δ TUV have an angle measuring 73°. Since both angles m∠ S in Δ QRS and m∠ V in Δ TUV are equal to 73°, we need to use this information along with other properties of the triangles.

3. Triangle Property:

Both given angles are within right triangles (right triangle Δ QRS and right triangle Δ TUV).

4. AA (Angle-Angle) Postulate:

According to the Angle-Angle (AA) similarity postulate, two triangles are similar if they have two corresponding angles that are congruent. Since both triangles include a right angle (90°) and they share another corresponding angle of 73°, the third angle in both triangles must also be equal, due to the angle sum property of triangles (sum of angles in a triangle is 180°).

Therefore, since both triangles share two corresponding congruent angles, they are similar by the AA (Angle-Angle) similarity postulate.

Conclusion:

The similarity postulate that proves Δ QRS and Δ TUV are similar is:

B. AA
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