Math Problem Statement
Based on the information given below, which two of the triangles below must be congruent? Enter your answer as a list of numbers. If you think the first and second triangles are congruent, enter "1,2".
[asy] size(15cm); pair A[]; pair B[]; pair C[]; pair nudge= (13,0); A[0] = (0,0); B[0] = (5,9); C[0] = (8,1); for(int i =1; i< 5; ++i){ A[i] = shift(nudge)A[i-1]; B[i] = shift(nudge)B[i-1]; C[i] = shift(nudge)C[i-1]; } for(int i =0; i<5; ++i){ draw(A[i]--B[i]--C[i]--cycle); label("$13$", (A[i]+B[i])/2, W); label("$12$", (B[i]+C[i])/2, E); } label(scale(0.75)"$62^{\circ}$", A[0]+0.65dir(35), dir(35)); label(scale(0.75)"$42^{\circ}$", C[1]+0.25dir(145), dir(145)); label(scale(0.75)"$40^{\circ}$", A[2]+0.65dir(35), dir(35)); label(scale(0.75)"$44^{\circ}$", C[2]+0.25dir(145), dir(145)); label(scale(0.75)"$45^{\circ}$", B[3]+1.25dir(-100), S); label(scale(0.75)"$73^{\circ}$", C[4]+0.25dir(145), dir(145)); label(scale(0.75)"$62^{\circ}$", A[4]+0.65*dir(35), dir(35)); [/asy] (Based on section 3.3 of the textbook.)
Solution
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Math Problem Analysis
Mathematical Concepts
Triangle Congruence
Geometry
ASA (Angle-Side-Angle) Congruence
Formulas
ASA (Angle-Side-Angle) Congruence Rule
Theorems
Congruence Theorems (ASA, SAS, SSS)
Suitable Grade Level
Grades 9-11
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