LESSON Angle Relationships in Triangles 4-2

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

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download