CK-12 Geometry - Second Edition

4.3. Triangle Congruence using SSS and SAS http://www.ck12.org

Solution:

TABLE4.6:

Statement Reason

1.Cis the midpoint ofAEandDB Given

2.AC∼=CE,BC∼=CD Definition of a midpoint

3.^6 ACB∼=^6 DCE Vertical Angles Postulate
4. 4 ACB∼= 4 ECD SAS Postulate

In Example 4, we could have only proven the two triangles congruent by SAS. If we were given thatAB∼=DE, then
we could have also proven the two triangles congruent by SSS.

SSS in the Coordinate Plane

In the coordinate plane, the easiest way to show two triangles are congruent is to find the lengths of the 3 sides in
each triangle. Finding the measure of an angle in the coordinate plane can be a little tricky, so we will avoid it in this
text. Therefore, you will only need to apply SSS in the coordinate plane. To find the lengths of the sides, you will

need to use the distance formula,

√

(x 2 −x 1 )^2 +(y 2 −y 1 )^2.

Example 5:Find the distances of all the line segments from both triangles to see if the two triangles are congruent.

Solution:Begin with 4 ABCand its sides.