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In the figure, A is the circumcenter of Δ LMN . Find y if LO = 8 y + 9 and ON = 12 y – 11. A. –5 B. 0.5 C. 5 D. 10. 5-Minute Check 1. In the figure, point D is the incenter of Δ ABC . What segment is congruent to DG ?. ___. ___. A. DE B. DA C. DC D. DB. ___. ___.
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In the figure, A is the circumcenter of ΔLMN. Find y if LO = 8y + 9 and ON = 12y – 11. A. –5 B. 0.5 C. 5 D. 10 5-Minute Check 1
In the figure, point D is the incenter of ΔABC. What segment is congruent to DG? ___ ___ A.DE B.DA C.DC D.DB ___ ___ ___ 5-Minute Check 4
In the figure, point D is the incenter of ΔABC. What angle is congruent to DCF? A. GCD B. DCG C. DFB D. ADE 5-Minute Check 5
Use the Centroid Theorem In ΔXYZ, P is the centroid and YV = 12. Find YP and PV. Centroid Theorem YV = 12 Simplify. Example 1
Use the Centroid Theorem YP + PV = YV Segment Addition 8 + PV = 12 YP = 8 PV = 4 Subtract 8 from each side. Answer:YP = 8; PV = 4 Example 1
In ΔLNP, R is the centroid and LO = 30. Find LR and RO. A.LR = 15; RO = 15 B.LR = 20; RO = 10 C.LR = 17; RO = 13 D.LR = 18; RO = 12 Example 1
Use the Centroid Theorem In ΔABC, CG = 4. Find GE. Example 2
Use the Centroid Theorem Centroid Theorem CG = 4 6 = CE Example 2
Use the Centroid Theorem CG + GE = CE Segment Addition 4 + GE = 6 Substitution GE = 2 Subtract 4 from each side. Answer:GE = 2 Example 2
In ΔJLN, JP = 16. Find PM. A. 4 B. 6 C. 16 D. 8 Example 2
