Incenter and Circumcenter Quiz
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- Cynthia Shelton
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1 Name: lass: ate: I: Incenter and ircumcenter Quiz Multiple hoice Identify the choice that best completes the statement or answers the question.. The diagram below shows the construction of the center of the circle circumscribed about. This construction represents how to find the intersection of a. the angle bisectors of b. the medians to the sides of c. the altitudes to the sides of d. the perpendicular bisectors of the sides of 2. Which geometric principle is used in the construction shown below? a. The intersection of the angle bisectors of a triangle is the center of the inscribed circle. b. The intersection of the angle bisectors of a triangle is the center of the circumscribed circle. c. The intersection of the perpendicular bisectors of the sides of a triangle is the center of the inscribed circle. d. The intersection of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle.
2 Name: I: 3. Three towns, Maybury, Junesville, and yanna, will create one sports center. Where should the center be placed so that it is the same distance from all three towns? a. Treat the towns as vertices of a triangle. The center must be placed at the triangle s b. Treat the towns as vertices of a triangle. The center must be placed at the triangle s c. Treat the towns as sides of a triangle. The center must be placed at the triangle s d. Treat the towns as sides of a triangle. The center must be placed at the triangle s 4. In the diagram below of, is the bisector of, E is the bisector of, and G is drawn. Which statement must be true? a. G = EG c. E E b. G = G d. G EG 5. ZO, YO, and XO are the perpendicular bisectors of. Find O. a. O = 4.2 c. O = 7.4 b. O = 3.4 d. O = 4.8 2
3 I: Incenter and ircumcenter Quiz nswer Section MULTIPLE HOIE. NS: PTS: 2 REF: ge ST: G.G.2 2. NS: PTS: 2 REF: 08028ge ST: G.G.2 3. NS: Let the three towns be vertices of a triangle. y the ircumcenter Theorem, the circumcenter of the triangle is equidistant from the vertices. To find the circumcenter, find the perpendicular bisectors of each side. Their intersection is the The center must be placed at the triangle's Treat the towns as vertices of a triangle. Treat the towns as vertices of a triangle. The center must be placed at the triangle's PTS: IF: verage REF: ad9a29e-4683-df-9c7d-0085f0d2ea OJ: pplication ST: NY.NYLES.MTH.05.GEO.G.G.2 KEY: circumcenter OK: OK 2 4. NS: G is also an angle bisector since it intersects the concurrence of and E PTS: 2 REF: 06025ge ST: G.G.2 KEY: entroid, Orthocenter, Incenter and ircumcenter 5. NS: O is the circumcenter of. y the ircumcenter Theorem, O is equidistant from the vertices of. O = O ircumcenter Theorem O = 4.2 Substitute 4.2 for O. PTS: IF: verage REF: ad df-9c7d-0085f0d2ea OJ: 5-2. Using Properties of Perpendicular isectors ST: NY.NYLES.MTH.05.GEO.G.G.2 KEY: perpendicular bisector circumcenter OK: OK
4 Name: lass: ate: I: Incenter and ircumcenter Quiz Multiple hoice Identify the choice that best completes the statement or answers the question.. The diagram below shows the construction of the center of the circle circumscribed about. This construction represents how to find the intersection of a. the altitudes to the sides of b. the perpendicular bisectors of the sides of c. the angle bisectors of d. the medians to the sides of 2. Which geometric principle is used in the construction shown below? a. The intersection of the angle bisectors of a triangle is the center of the inscribed circle. b. The intersection of the angle bisectors of a triangle is the center of the circumscribed circle. c. The intersection of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle. d. The intersection of the perpendicular bisectors of the sides of a triangle is the center of the inscribed circle.
5 Name: I: 3. Three towns, Maybury, Junesville, and yanna, will create one sports center. Where should the center be placed so that it is the same distance from all three towns? a. Treat the towns as vertices of a triangle. The center must be placed at the triangle s b. Treat the towns as sides of a triangle. The center must be placed at the triangle s c. Treat the towns as vertices of a triangle. The center must be placed at the triangle s d. Treat the towns as sides of a triangle. The center must be placed at the triangle s 4. In the diagram below of, is the bisector of, E is the bisector of, and G is drawn. Which statement must be true? a. G = G c. G = EG b. G EG d. E E 5. ZO, YO, and XO are the perpendicular bisectors of. Find O. a. O = 4.2 c. O = 4.8 b. O = 3.4 d. O = 7.4 2
6 I: Incenter and ircumcenter Quiz nswer Section MULTIPLE HOIE. NS: PTS: 2 REF: ge ST: G.G.2 2. NS: PTS: 2 REF: 08028ge ST: G.G.2 3. NS: Let the three towns be vertices of a triangle. y the ircumcenter Theorem, the circumcenter of the triangle is equidistant from the vertices. To find the circumcenter, find the perpendicular bisectors of each side. Their intersection is the The center must be placed at the triangle's Treat the towns as vertices of a triangle. The center must be placed at the triangle's Treat the towns as vertices of a triangle. PTS: IF: verage REF: ad9a29e-4683-df-9c7d-0085f0d2ea OJ: pplication ST: NY.NYLES.MTH.05.GEO.G.G.2 KEY: circumcenter OK: OK 2 4. NS: G is also an angle bisector since it intersects the concurrence of and E PTS: 2 REF: 06025ge ST: G.G.2 KEY: entroid, Orthocenter, Incenter and ircumcenter 5. NS: O is the circumcenter of. y the ircumcenter Theorem, O is equidistant from the vertices of. O = O ircumcenter Theorem O = 4.2 Substitute 4.2 for O. PTS: IF: verage REF: ad df-9c7d-0085f0d2ea OJ: 5-2. Using Properties of Perpendicular isectors ST: NY.NYLES.MTH.05.GEO.G.G.2 KEY: perpendicular bisector circumcenter OK: OK
7 Name: lass: ate: I: Incenter and ircumcenter Quiz Multiple hoice Identify the choice that best completes the statement or answers the question.. The diagram below shows the construction of the center of the circle circumscribed about. This construction represents how to find the intersection of a. the angle bisectors of b. the perpendicular bisectors of the sides of c. the medians to the sides of d. the altitudes to the sides of 2. Which geometric principle is used in the construction shown below? a. The intersection of the angle bisectors of a triangle is the center of the circumscribed circle. b. The intersection of the perpendicular bisectors of the sides of a triangle is the center of the inscribed circle. c. The intersection of the angle bisectors of a triangle is the center of the inscribed circle. d. The intersection of the perpendicular bisectors of the sides of a triangle is the center of the circumscribed circle.
8 Name: I: 3. Three towns, Maybury, Junesville, and yanna, will create one sports center. Where should the center be placed so that it is the same distance from all three towns? a. Treat the towns as vertices of a triangle. The center must be placed at the triangle s b. Treat the towns as vertices of a triangle. The center must be placed at the triangle s c. Treat the towns as sides of a triangle. The center must be placed at the triangle s d. Treat the towns as sides of a triangle. The center must be placed at the triangle s 4. In the diagram below of, is the bisector of, E is the bisector of, and G is drawn. Which statement must be true? a. G = EG c. E E b. G = G d. G EG 5. ZO, YO, and XO are the perpendicular bisectors of. Find O. a. O = 7.4 c. O = 3.4 b. O = 4.2 d. O = 4.8 2
9 I: Incenter and ircumcenter Quiz nswer Section MULTIPLE HOIE. NS: PTS: 2 REF: ge ST: G.G.2 2. NS: PTS: 2 REF: 08028ge ST: G.G.2 3. NS: Let the three towns be vertices of a triangle. y the ircumcenter Theorem, the circumcenter of the triangle is equidistant from the vertices. To find the circumcenter, find the perpendicular bisectors of each side. Their intersection is the The center must be placed at the triangle's Treat the towns as vertices of a triangle. The center must be placed at the triangle's Treat the towns as vertices of a triangle. PTS: IF: verage REF: ad9a29e-4683-df-9c7d-0085f0d2ea OJ: pplication ST: NY.NYLES.MTH.05.GEO.G.G.2 KEY: circumcenter OK: OK 2 4. NS: G is also an angle bisector since it intersects the concurrence of and E PTS: 2 REF: 06025ge ST: G.G.2 KEY: entroid, Orthocenter, Incenter and ircumcenter 5. NS: O is the circumcenter of. y the ircumcenter Theorem, O is equidistant from the vertices of. O = O ircumcenter Theorem O = 4.2 Substitute 4.2 for O. PTS: IF: verage REF: ad df-9c7d-0085f0d2ea OJ: 5-2. Using Properties of Perpendicular isectors ST: NY.NYLES.MTH.05.GEO.G.G.2 KEY: perpendicular bisector circumcenter OK: OK
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