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McGraw Hill Glencoe Geometry, 2012 View details

6. Isosceles and Equilateral Triangles

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Exercise 8 Page 289

A

a

Statements	Reasons
QR ⊥ QT, ST ⊥ QT, QT∥ SR, △ VSR is isosceles with base SR, and QT∥ SR	Given
∠ RQV and ∠ STV are right angles	Definition of perpendicular lines
∠ RQV ≅ ∠ STV	All the right angles are congruent
VR ≅ VS	Definition of isosceles
∠ VSR ≅ ∠ VRS	Isosceles Triangle Theorem
∠ QVR ≅ ∠ VRS and ∠ TVS ≅ ∠ VSR	Alternate Interior Angle Theorem
∠ QVR ≅ ∠ TVS	Transitive Property of Congruence
△ RQV ≅ △ STV	Angle-Angle-Side Theorem