Question
In the figure above, the triangles are congruent by ASA. Complete the congruence statement. Triangle RPQ is congruent to triangle
Ask by Perkins Reese. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Triangle RPQ is congruent to triangle XYZ.
Solution
To complete the congruence statement for the triangles, we need to identify the corresponding vertices of triangle RPQ based on the ASA (Angle-Side-Angle) congruence criterion.
Since triangle RPQ is congruent to another triangle, we can denote the vertices of the other triangle as follows:
- The vertex R corresponds to the vertex that is opposite to the angle at vertex R in the other triangle.
- The vertex P corresponds to the vertex that is opposite to the angle at vertex P in the other triangle.
- The vertex Q corresponds to the vertex that is opposite to the angle at vertex Q in the other triangle.
Assuming the other triangle is named XYZ, the congruence statement can be completed as:
\[
\triangle RPQ \cong \triangle XYZ
\]
If you have specific labels for the other triangle, please provide them, and I can adjust the congruence statement accordingly.
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Simplify this solution The Deep Dive
Triangle RPQ is congruent to triangle SQT. In congruence statements, the order of the vertices is important, reflecting the corresponding angles and sides. Since you established the congruence using the ASA (Angle-Side-Angle) postulate, it indicates that the angles and the included side are correctly aligned between both triangles. To strengthen your understanding, remember that congruent triangles have exactly the same shape and size. This means not only that corresponding angles are equal, but also that corresponding sides are proportional and congruent. So in any proof or problem involving triangles, always look for shortcuts like ASA to simplify your work!
