NSTSE (National Science Talent Search Exam- Unified Council) Class 4: Questions 1182 - 1182 of 1971

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Question number: 1182

» Mathematics » Geometry

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Question

Which of the following figures contains exactly four triangles?

Choices

Choice (4)Response

a.

Quadrilateral poly1Quadrilateral poly1: Polygon A, B, C, DTriangle poly2Triangle poly2: Polygon E, F, GQuadrilateral poly3Quadrilateral poly3: Polygon H, I, J, KQuadrilateral poly3_1Quadrilateral poly3_1: Polygon H_1, I_1, J_1, K_1Triangle poly4Triangle poly4: Polygon N, O, PQuadrilateral poly3_2Quadrilateral poly3_2: Polygon H_2, I_2, J_2, K_2Circle pCircle p: Circle through M with center LCircle pCircle p: Circle through M with center LCircle p_1Circle p_1: Circle through M_1 with center L_1Circle p_1Circle p_1: Circle through M_1 with center L_1Segment aSegment a: Segment [A, B] of Quadrilateral poly1Segment bSegment b: Segment [B, C] of Quadrilateral poly1Segment cSegment c: Segment [C, D] of Quadrilateral poly1Segment dSegment d: Segment [D, A] of Quadrilateral poly1Segment gSegment g: Segment [E, F] of Triangle poly2Segment eSegment e: Segment [F, G] of Triangle poly2Segment fSegment f: Segment [G, E] of Triangle poly2Segment hSegment h: Segment [H, I] of Quadrilateral poly3Segment iSegment i: Segment [I, J] of Quadrilateral poly3Segment jSegment j: Segment [J, K] of Quadrilateral poly3Segment kSegment k: Segment [K, H] of Quadrilateral poly3Segment h_1Segment h_1: Segment [H_1, I_1] of Quadrilateral poly3_1Segment i_1Segment i_1: Segment [I_1, J_1] of Quadrilateral poly3_1Segment j_1Segment j_1: Segment [J_1, K_1] of Quadrilateral poly3_1Segment k_1Segment k_1: Segment [K_1, H_1] of Quadrilateral poly3_1Segment p_2Segment p_2: Segment [N, O] of Triangle poly4Segment nSegment n: Segment [O, P] of Triangle poly4Segment oSegment o: Segment [P, N] of Triangle poly4Segment h_2Segment h_2: Segment [H_2, I_2] of Quadrilateral poly3_2Segment i_2Segment i_2: Segment [I_2, J_2] of Quadrilateral poly3_2Segment j_2Segment j_2: Segment [J_2, K_2] of Quadrilateral poly3_2Segment k_2Segment k_2: Segment [K_2, H_2] of Quadrilateral poly3_2

This Image Shows the Basic Shapes – Choice A

b.

Quadrilateral poly1Quadrilateral poly1: Polygon C, D, E, FQuadrilateral poly2Quadrilateral poly2: Polygon G, H, I, JQuadrilateral poly2_1Quadrilateral poly2_1: Polygon G_1, H_1, I_1, J_1Triangle poly3Triangle poly3: Polygon M, N, OQuadrilateral poly4Quadrilateral poly4: Polygon P, Q, R, SCircle cCircle c: Circle through B with center ACircle cCircle c: Circle through B with center ACircle kCircle k: Circle through L with center KCircle kCircle k: Circle through L with center KCircle k_1Circle k_1: Circle through L_1 with center K_1Circle k_1Circle k_1: Circle through L_1 with center K_1Segment c_1Segment c_1: Segment [C, D] of Quadrilateral poly1Segment dSegment d: Segment [D, E] of Quadrilateral poly1Segment eSegment e: Segment [E, F] of Quadrilateral poly1Segment fSegment f: Segment [F, C] of Quadrilateral poly1Segment gSegment g: Segment [G, H] of Quadrilateral poly2Segment hSegment h: Segment [H, I] of Quadrilateral poly2Segment iSegment i: Segment [I, J] of Quadrilateral poly2Segment jSegment j: Segment [J, G] of Quadrilateral poly2Segment g_1Segment g_1: Segment [G_1, H_1] of Quadrilateral poly2_1Segment h_1Segment h_1: Segment [H_1, I_1] of Quadrilateral poly2_1Segment i_1Segment i_1: Segment [I_1, J_1] of Quadrilateral poly2_1Segment j_1Segment j_1: Segment [J_1, G_1] of Quadrilateral poly2_1Segment oSegment o: Segment [M, N] of Triangle poly3Segment mSegment m: Segment [N, O] of Triangle poly3Segment nSegment n: Segment [O, M] of Triangle poly3Segment pSegment p: Segment [P, Q] of Quadrilateral poly4Segment qSegment q: Segment [Q, R] of Quadrilateral poly4Segment rSegment r: Segment [R, S] of Quadrilateral poly4Segment sSegment s: Segment [S, P] of Quadrilateral poly4

This Image Shows the Basic Shapes – Choice B

c.

Triangle poly1Triangle poly1: Polygon A, B, CTriangle poly2Triangle poly2: Polygon D, E, FTriangle poly2_1Triangle poly2_1: Polygon D_1, E_1, F_1Triangle poly2_2Triangle poly2_2: Polygon D_2, E_2, F_2Quadrilateral poly3Quadrilateral poly3: Polygon I, J, K, LQuadrilateral poly3_1Quadrilateral poly3_1: Polygon I_1, J_1, K_1, L_1Quadrilateral poly3_2Quadrilateral poly3_2: Polygon I_2, J_2, K_2, L_2Circle gCircle g: Circle through H with center GCircle gCircle g: Circle through H with center GSegment cSegment c: Segment [A, B] of Triangle poly1Segment aSegment a: Segment [B, C] of Triangle poly1Segment bSegment b: Segment [C, A] of Triangle poly1Segment fSegment f: Segment [D, E] of Triangle poly2Segment dSegment d: Segment [E, F] of Triangle poly2Segment eSegment e: Segment [F, D] of Triangle poly2Segment f_1Segment f_1: Segment [D_1, E_1] of Triangle poly2_1Segment d_1Segment d_1: Segment [E_1, F_1] of Triangle poly2_1Segment e_1Segment e_1: Segment [F_1, D_1] of Triangle poly2_1Segment f_2Segment f_2: Segment [D_2, E_2] of Triangle poly2_2Segment d_2Segment d_2: Segment [E_2, F_2] of Triangle poly2_2Segment e_2Segment e_2: Segment [F_2, D_2] of Triangle poly2_2Segment iSegment i: Segment [I, J] of Quadrilateral poly3Segment jSegment j: Segment [J, K] of Quadrilateral poly3Segment kSegment k: Segment [K, L] of Quadrilateral poly3Segment lSegment l: Segment [L, I] of Quadrilateral poly3Segment i_1Segment i_1: Segment [I_1, J_1] of Quadrilateral poly3_1Segment j_1Segment j_1: Segment [J_1, K_1] of Quadrilateral poly3_1Segment k_1Segment k_1: Segment [K_1, L_1] of Quadrilateral poly3_1Segment l_1Segment l_1: Segment [L_1, I_1] of Quadrilateral poly3_1Segment i_2Segment i_2: Segment [I_2, J_2] of Quadrilateral poly3_2Segment j_2Segment j_2: Segment [J_2, K_2] of Quadrilateral poly3_2Segment k_2Segment k_2: Segment [K_2, L_2] of Quadrilateral poly3_2Segment l_2Segment l_2: Segment [L_2, I_2] of Quadrilateral poly3_2

This Image Shows the Basic Shapes – Choice C

d.

Triangle poly1Triangle poly1: Polygon A, B, CQuadrilateral poly2Quadrilateral poly2: Polygon D, E, F, GQuadrilateral poly3Quadrilateral poly3: Polygon J, K, L, MQuadrilateral poly3_1Quadrilateral poly3_1: Polygon J_1, K_1, L_1, M_1Triangle poly4Triangle poly4: Polygon N, O, PQuadrilateral poly5Quadrilateral poly5: Polygon Q, R, S, TCircle hCircle h: Circle through I with center HCircle hCircle h: Circle through I with center HCircle h_1Circle h_1: Circle through I_1 with center H_1Circle h_1Circle h_1: Circle through I_1 with center H_1Segment cSegment c: Segment [A, B] of Triangle poly1Segment aSegment a: Segment [B, C] of Triangle poly1Segment bSegment b: Segment [C, A] of Triangle poly1Segment dSegment d: Segment [D, E] of Quadrilateral poly2Segment eSegment e: Segment [E, F] of Quadrilateral poly2Segment fSegment f: Segment [F, G] of Quadrilateral poly2Segment gSegment g: Segment [G, D] of Quadrilateral poly2Segment jSegment j: Segment [J, K] of Quadrilateral poly3Segment kSegment k: Segment [K, L] of Quadrilateral poly3Segment lSegment l: Segment [L, M] of Quadrilateral poly3Segment mSegment m: Segment [M, J] of Quadrilateral poly3Segment j_1Segment j_1: Segment [J_1, K_1] of Quadrilateral poly3_1Segment k_1Segment k_1: Segment [K_1, L_1] of Quadrilateral poly3_1Segment l_1Segment l_1: Segment [L_1, M_1] of Quadrilateral poly3_1Segment m_1Segment m_1: Segment [M_1, J_1] of Quadrilateral poly3_1Segment pSegment p: Segment [N, O] of Triangle poly4Segment nSegment n: Segment [O, P] of Triangle poly4Segment oSegment o: Segment [P, N] of Triangle poly4Segment qSegment q: Segment [Q, R] of Quadrilateral poly5Segment rSegment r: Segment [R, S] of Quadrilateral poly5Segment sSegment s: Segment [S, T] of Quadrilateral poly5Segment tSegment t: Segment [T, Q] of Quadrilateral poly5

This Image Shows the Basic Shapes – Choice D

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