Question

Plane M is the perpendicular bisecting plane of at O (that is, M is the plane that is perpendicular to at its midpoint, O). Points C and D also lie in plane M. List three pairs of congruent triangles and tell which congruence method can be used to prove each pair congruent.

Short answer

Three pairs of congruent triangles are

Step-by-step solution

- Show that  

Since, point lies on a plane which is perpendicular to

So, are of each

Statement	Reason
1.	Given
2.	Each
3.	Reflexive property
4.	SAS(Side-Angle-Side) postulate

- Show that  

Since, point lies on a plane which is perpendicular to

So, are of each

Statement	Reason
1.	Given
2.	Each
3.	Reflexive property
4.	SAS(Side-Angle-Side) postulate

- Show that  

Since, corresponding parts of congruent triangle is congruent

So, from step 1 and 2

Statement	Reason
1.$\overline{AD}\cong \overline{BD}$	As $∆AOD\cong ∆BOD$
2.$\overline{AC}\cong \overline{BC}$	As$∆AOC\cong ∆BOD$
3.$\overline{CD}\cong \overline{CD}$	Reflexive property
4.$∆ACD\cong ∆BCD$	SSS(Side-Side-Side) postulate