Math Problem Statement
Complete the proof.
A triangle has three labeled vertices, two labeled points, and two line segments. The bottom side of the triangle is horizontal, starts at vertex P at left and ends at vertex Q at right. Vertex S is above and right of P and above and left of Q. The left side starts at vertex S and ends at vertex P. Between S and P lies point T. The right side starts at vertex S and ends at vertex Q. Between S and Q lies point V. The first line segment starts at vertex Q, goes up and to the left, passes through a second line segment at an unlabeled point, and ends at point T. The second line segment starts at vertex P, goes up and to the right, passes through the first line segment at an unlabeled point, and ends at point V. Given: SP ≅ SQ and ST ≅ SV Prove: △SPV ≅ △SQT and △TPQ ≅ △VQP Statements Reasons 1. SP ≅ SQ; ST ≅ SV 1. Given 2. ---Select--- 2. ---Select--- 3. ---Select--- 3. ---Select--- 4. PV ≅ QT 4. ---Select--- 5. PQ ≅ PQ 5. ---Select--- 6. ---Select--- 6. If segments are ≅, they are = in measure. 7. ---Select--- 7. ---Select--- 8. ---Select--- 8. Substitution 9. ---Select--- 9. Substitution 10. ---Select--- 10. ---Select--- 11. PT ≅ QV 11. ---Select--- 12. ---Select--- 12. ---Select---
Solution
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Math Problem Analysis
Mathematical Concepts
Triangle Congruence
Isosceles Triangles
Geometric Proofs
Formulas
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Theorems
Side-Angle-Side (SAS) Postulate
Corresponding Parts of Congruent Triangles (CPCTC)
Vertical Angles Theorem
Suitable Grade Level
Grades 9-12