CCSS HSG-CO.C.9 Worksheets
Geometry · Congruence
Prove line-and-angle theorems, including vertical-angle congruence, angle relationships created when a transversal crosses parallel lines, and the equidistance property of a segment's perpendicular bisector.
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Deliver a whole lesson on HSG-CO.C.9 from a textbook-grade teaching unit, with a hook, worked examples, diagrams, misconceptions, and an exit ticket.
Teaching guide
Prove line-and-angle theorems, including vertical-angle congruence, angle relationships created when a transversal crosses parallel lines, and the equidistance property of a segment's perpendicular bisector.
| Statement | Reason |
|---|---|
| 1.B, O, D are collinear, and C, O, A are collinear. | Given |
| 2.∠BOC and ∠COD form a linear pair. | Definition of a linear pair (BOD is a straight line) |
| 3.∠COD and ∠DOA form a linear pair. | Definition of a linear pair (COA is a straight line) |
| 4.m∠BOC + m∠COD = 180°, and m∠COD + m∠DOA = 180°. | Linear Pair Postulate |
| 5.m∠BOC + m∠COD = m∠COD + m∠DOA. | Transitive Property of Equality |
| 6.m∠BOC = m∠DOA. | Subtraction Property of Equality |
| 7.∠BOC ≅ ∠DOA. | Definition of congruent angles |
Generated and checked in code, so it is correct.