Question

Given: ADCB, and MD ME

Prove: AM = CM
D
B
OA
AMDA
OB. AMDA
M
Statements
Reasons
ZDMA ZBMC vertical angles theorem
MD MB
given
AD || CB
given
ZMDA
MBC alternate interior angles theorem
?
AM CM
AM = CM
Which step is missing in the proof?
?
CPCTC
definition of congruence
AMCB by ASA
AMBC by SAS

Answer 1

1. angle DMA = angle BMC : vertical angles theorem

2. MD is congruent to MB : given

3. angle MDA is congruent to angle MBC ( alternate interior angles)

4. Triangle MDA is congruent to triangle MBC : by ASA postulate of congruency. ( option A)

What are congruent triangles?

Congruent triangles have corresponding angles and sides equal in measure. They are identical when superimposed, maintaining the same shape and size.

1. angle DMA = angle BMC : vertical angles theorem

2. MD is congruent to MB : given

3. angle MDA is congruent to angle MBC ( alternate interior angles)

4. Triangle MDA is congruent to triangle MBC : by ASA postulate of congruency.