Question

In the figure above CD is the perpendicular bisector of AB. three students explained how they proved ADC is congruent to BDC

Answer 1

Answer:

All three explanations are correct.

Step-by-step explanation:

In the given triangles CD is perpendicular bisector of AB

So we have

AC= BC  ( C is on perpendicular bisector of AB and hence C is equidistant              from A and B)

∠ADC =∠BDC =90°                 ( CD ⊥ AB)

CD = CD   ( reflexive property)

AD = BD  (  CD is bisects AB)

We can use HL theorem or  SSS or SAS  to prove ΔADC≅ΔBDC

Hence all the three explanations are correct.

Answer 2

Answer:

All explanations are correct

Step-by-step explanation:

In triangle ABC, CD is the perpendicular bisector of AB, thus using ΔADC and ΔBDC,

AC=BC ( Since CD is perpendicular to AB, therefore C is equidistant from both A and B)

∠ADC=∠BDC=90°(CD perpendicular AB)

CD=CD( Reflexive property)

therefore, by SAS rule of congruency,

ΔADC≅ ΔBDC,

Also, In the same triangles, AC=BC ( Since CD is perpendicular to AB, therefore C is equidistant from both A and B)

CD=CD( Reflexive property)

AD=BD (D is the midpoint and divides AB into two equal halves)

Thus, by SSS rule of congruency,

ΔADC≅ ΔBDC,

Thus, all the three explanations are correct.