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Copy and complete the proof.

The statements in Exercise 2 might be used as statements in a proof but they are given out of order. Find an appropriate order for the statements. (There may be more than one correct order.)

2. Given:AMBM,TMAB

Prove:ATBT

(a)AMBM(b)AMTBMT(c)12(d)ATBT(e)TMAB(f)TMTM

Short Answer

Expert verified

(a)AMBM(b)TMAB(c)12(d)TMTM(e)AMTBMT(f)ATBT

Step by step solution

01

- Write concept used

The two triangles are said to be congruent if they are copies of each other and if their vertices are superposed, then say that corresponding angles and the sides of the triangles are congruent.

Congruency of triangles can be proved by SSS, SAS and ASA, AAS and HL postulates.

To prove that two segments or two angles are congruent, firstly identity the two triangles in which that two segments or angles are corresponding parts. After that, prove that the identified triangles are congruent and then, state that the two parts are congruent using the reason 鈥淐orresponding parts of triangles are 鈥.

02

- Show ΔAMT≅ΔBMT

Since, perpendicular lines forms congruent adjacent angles at the intersection

So, 12

Moreover in triangles role="math" localid="1648819242586" AMTand BMT, TMTMas it is the common line segment.

So using given statement along with this statement givesAMTBMT

03

- Show AT¯≅BT¯

Since, corresponding parts of congruent triangles are congruent

So,ATBT

Hence, correct order will be

(a)AMBM(b)TMAB(c)12(d)TMTM(e)AMTBMT(f)ATBT

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