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40 votes
solve the problems. write the complete proof in your paper homework and for online (only) complete the probing statement (if any) that is a part of your proof or related to it

solve the problems. write the complete proof in your paper homework and for online-example-1
User Andreas Rossberg
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2 Answers

17 votes
17 votes

m∠A ≅ m∠C by reason Base angles theorem

△ AMO≅△ CPO by reason ASA / SAA

solve the problems. write the complete proof in your paper homework and for online-example-1
User Gauravg
by
2.8k points
15 votes
15 votes

Answer:


m \angle A = m \angle C by reason
\overline{AB} \cong \overline{BC} and
m \angle B = m \angle M = m \angle P.


\triangle AMO \cong \triangle CPO SAS Theorem

Explanation:

We proceed to demonstrate the statement by Geometric means:

1)
\overline{AB} \cong \overline{BC},
\overline {AM} \cong \overline {PC},
m\angle AMO = m\angle CPO Given.

2)
(AM)/(AB) = (PC)/(BC) Proportionality.

3)
(AM)/(AM + MB) = (PC)/(BP + PC) Definition of line segments.

4)
(1)/(1+(MB)/(AM) ) = (1)/((BP)/(PC)+1) Algebra.

5)
(BP)/(PC) + 1 = 1 +(MB)/(AM) Algebra.

6)
(BP)/(PC) = (MB)/(AM) Algebra.

7)
BP = BM By 1)

8)
m \angle B = m \angle M = m \angle P By 1), 7)

9)
\triangle AMO \sim \triangle ABC,
\triangle CPO \sim \triangle ABC By 1), 7), 8). Defintion of simmilarity.

10)
(AM)/(MO) = (AB)/(BC),
(PO)/(PC) = (AB)/(BC) Definition of proportionality.

11)
(AM)/(MO) = (PO)/(PC) Algebra.

12)
AM^(2) = PO\cdot MO Algebra.

13)
PO = MO By 12) and Algebra.

14)
\overline{PO} \cong \overline{MO} By 13).

15)
\triangle AMO \cong \triangle CPO SAS Theorem/Result.

User HISI
by
3.2k points
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