LESSON Angle Relationships in Triangles 4-2 - Welcome to Mrs ...
LESSON Angle Relationships in Triangles 4-2
Lesson Objectives (p. 223): ______________________________________________________________ ______________________________________________________________
Vocabulary 1. Auxiliary line (p. 223): ____________________________________________ ______________________________________________________________ 2. Corollary (p. 224): _______________________________________________ ______________________________________________________________ 3. Interior (p. 225): _________________________________________________ ______________________________________________________________ 4. Exterior (p. 225): ________________________________________________ ______________________________________________________________ 5. Interior angle (p. 225): ____________________________________________ ______________________________________________________________ 6. Exterior angle (p. 225): ___________________________________________ ______________________________________________________________ 7. Remote interior angle (p. 225): _____________________________________ ______________________________________________________________
Copyright ? by Holt, Rinehart and Winston. All rights reserved.
79
Geometry
LESSON Angle Relationships in Triangles 4-2
Lesson Objectives (p. 223): _fin_d__t_h_e_m__e_a_su_r_e_s__o_f _in_te_r_i_o_r _a_n_d_e_x_t_e_ri_o_r _a_n_g_le_s__o_f _tr_ia_n_g_l_e_s;_a_p_p_l_y_t_h_e_o_re_m__s_ _a_b_o_u_t _th_e__in_t_e_ri_o_r _a_n_d_e_x_t_e_ri_o_r _a_n_g_le_s__o_f _tr_ia_n_g_l_e_s_. ______________________
Vocabulary 1. Auxiliary line (p. 223): _a_li_n_e_t_h_a_t_is__a_d_d_e_d_t_o_a__fi_g_u_re__to__a_id__in__a_p_r_o_o_f_. ______ ______________________________________________________________ 2. Corollary (p. 224): _a_t_h_e_o_re_m__w__h_o_se__p_r_o_o_f _fo_ll_o_w_s__d_ir_e_ct_ly__fr_o_m__a_n_o_th_e_r______ _th_e_o_r_e_m_._______________________________________________________ 3. Interior (p. 225): _th_e__s_e_t _o_f _a_ll_p_o_in_t_s_i_n_s_id_e__th_e__fig_u_r_e_.____________________ ______________________________________________________________ 4. Exterior (p. 225): _th_e__se_t__o_f _a_ll_p_o_in_t_s_o_u_t_s_id_e__th_e__fi_g_u_re_.__________________ ______________________________________________________________ 5. Interior angle (p. 225): a_n__a_n_g_le__fo_r_m__e_d_b_y__tw_o__s_id_e_s__o_f _a_t_ri_a_n_g_le_.__________ ______________________________________________________________ 6. Exterior angle (p. 225): _th_e__a_n_g_le__fo_r_m_e_d__b_y_o_n_e__s_id_e__o_f _th_e__tr_ia_n_g_l_e_a_n_d__th_e__ _e_xt_e_n_s_io_n__o_f _a_n_a_d_j_a_c_e_n_t _s_id_e_.______________________________________ 7. Remote interior angle (p. 225): _a_n_i_n_te_r_io_r_a_n_g_l_e_t_h_a_t _is__n_o_t _a_d_ja_c_e_n_t_to__t_h_e___ _e_xt_e_r_io_r_a_n_g_l_e.___________________________________________________
Copyright ? by Holt, Rinehart and Winston. All rights reserved.
79
Geometry
LESSON 4-2 CONTINUED
Key Concepts 8. Theorem 4-2-1--Triangle Sum Theorem (p. 223): Theorem 4-2-1
9. Corollaries (p. 224): Corollary 4-2-2
HYPOTHESIS CONCLUSION
4-2-3
10. Theorem 4-2-4--Exterior Angle Theorem (p. 225): Theorem 4-2-4
Copyright ? by Holt, Rinehart and Winston. All rights reserved.
80
Geometry
LESSON 4-2 CONTINUED
Key Concepts 8. Theorem 4-2-1--Triangle Sum Theorem (p. 223):
Theorem 4-2-1
The sum of the angle measures of a triangle is 180?. mA mB mC 180?
2
1
3
9. Corollaries (p. 224):
Corollary
HYPOTHESIS
4-2-2 The acute angles of a right triangle are complementary.
D
F
E
CONCLUSION
D E are complementary. mD mE 90?
4-2-3 The measure of
each angle of an
equilateral triangle
is 60?.
B
A
mA mB mC 60?
C
10. Theorem 4-2-4--Exterior Angle Theorem (p. 225):
Theorem 4-2-4
The measure on an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles. m4 m1 m2
2
1
34
Copyright ? by Holt, Rinehart and Winston. All rights reserved.
80
Geometry
LESSON 4-2 CONTINUED
11. Theorem 4-2-5--Third Angles Theorem (p. 226):
THEOREM
HYPOTHESIS
CONCLUSION
12. Get organized In each box, write each theorem in words and then draw a diagram to represent it. (p. 226).
THEOREM
Triangle Sum Theorem
WORDS
DIAGRAM
Exterior Angle Theorem
Third Angles Theorem
Copyright ? by Holt, Rinehart and Winston. All rights reserved.
81
Geometry
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