CCSS HSG-CO.C.10 Worksheets
Geometry · Congruence
Prove triangle theorems, including the 180-degree interior-angle sum, congruent base angles in an isosceles triangle, the triangle midsegment result, and concurrence of the medians.
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Deliver a whole lesson on HSG-CO.C.10 from a textbook-grade teaching unit, with a hook, worked examples, diagrams, misconceptions, and an exit ticket.
Teaching guide
Prove triangle theorems, including the 180-degree interior-angle sum, congruent base angles in an isosceles triangle, the triangle midsegment result, and concurrence of the medians.
| Statement | Reason |
|---|---|
| 1.△RPQ is a triangle. | Given |
| 2.Draw line n through Q, parallel to line RP. | Construction (Parallel Postulate) |
| 3.∠1 ≅ ∠R and ∠2 ≅ ∠P (∠1 and ∠2 are the angles n makes with QR and QP, on either side of ∠Q). | Alternate Interior Angles Theorem |
| 4.m∠1 = m∠R and m∠2 = m∠P. | Definition of congruent angles |
| 5.m∠1 + m∠RQP + m∠2 = 180°. | Angles on a straight line sum to 180° |
| 6.m∠R + m∠Q + m∠P = 180°. | Substitution Property of Equality |
| 7.m∠R + m∠P + m∠Q = 180°. | Commutative Property of Addition |
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