Choose from the following reasons below to prove the theorem. Some of them can be used twice. Factoring Addition property of equality Given The arc of the whole circle is 360º Inscribed angle theorem Definition of supplementary angles Substitution (steps 5 and 5) Algebraic process (step 6) Theorem: "If a quadrilateral in inscribed in a circle, then its opposite angles are supplementary." Given: Quadrilateral ABCD is inscribed in OE. Prove: ZADC and LABC are supplementary ZDAB and ZDCB are supplementary STATEMENT REASON 1. Quadrilateral ABCD is inscribed in OE. (1) 2. MLADC = =MABC (2) 1 MLABC =mĀDC 1 M2DAB = MDCB 1 MLDCB =MDAB Addition property of equality 3. MLADC + MLABC = MĀBC + MADC

Choose from the following reasons below to prove the theorem. Some of them can be used twice. Factoring Addition property of equality Given The arc of the whole circle is 360º Inscribed angle theorem Definition of supplementary angles Substitution (steps 5 and 5) Algebraic process (step 6) Theorem: "If a quadrilateral in inscribed in a circle, then its opposite angles are supplementary." Given: Quadrilateral ABCD is inscribed in OE. Prove: ZADC and LABC are supplementary ZDAB and ZDCB are supplementary STATEMENT REASON 1. Quadrilateral ABCD is inscribed in OE. (1) 2. MLADC = =MABC (2) 1 MLABC =mĀDC 1 M2DAB = MDCB 1 MLDCB =MDAB Addition property of equality 3. MLADC + MLABC = MĀBC + MADC

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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LEARNING TASK 3
Choose from the following reasons below to prove the theorem. Some of them can
be used twice.
Factoring
Addition property of equality
Given
The arc of the whole circle is 360°
Inscribed angle theorem
Definition of supplementary angles
Substitution (steps 5 and 5)
Algebraic process (step 6)
Theorem: "If a quadrilateral in inscribed in a circle, then its opposite angles are
supplementary."
Given: Quadrilateral ABCD is inscribed in OE.
Prove: ZADC and ZABC are supplementary
ZDAB and ZDCB are supplementary
STATEMENT
1. Quadrilateral ABCD is inscribed in OE.
REASON
(1)
(2)
2. MLADC = =MABC
1
MADC
MLABC
M2DAB = ,ml
=-MDCB
1
MLDCB =MDAB
2.
Addition property of
equality
3. MLADC + MLABC
MĀBC +
-MĀDC

(3)
4. MLADC + MLABC =(MABC +
MĀDC)
5. MABC + MADC = 360
6. MLADC + MLABC =(360)
7. MLADC + MLABC = 180
8. LADC and LABC are supplementary
9. MLDAB + MLDCB =MDCB +
(4)
Substitution (steps 4 and 5)
Algebraic process (step 6)
(5)
(6)
MDAB
10. MLDAB + M2DCB =(MDCB +
MDAB)
11. MDCB + .DAB = 360
Factoring
%3D
(7)
(8)
12. MLDAB + MLDCB =(360)
13. MLDAB + M2DCB = 180
(9)
(10)
%3D
14. ZDAB and ZDCB are supplementary

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