CK-12 Geometry - Second Edition

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

TABLE4.5:

Statement Reason

1.AB∼=DE

Cis the midpoint ofAEandDB

Given

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

3. 4 ACB∼= 4 ECD SSS Postulate

Make sure that you clearly state the three sets of congruent sides BEFORE stating that the triangles are congruent.

Prove Move:Feel free to mark the picture with the information you are given as well as information that you can
infer (vertical angles, information from parallel lines, midpoints, angle bisectors, right angles).

SAS Triangle Congruence Postulate

First, it is important to note that SAS refers to Side-Angle-Side. The placement of the word Angle is important
because it indicates that the angle that you are given is between the two sides.

Included Angle:When an angle is between two given sides of a triangle (or polygon).

In the picture to the left, the markings indicate thatABandBCare the given sides, so^6 Bwould be the included
angle.

Consider the question: If I have two sides of length 2 in and 5 in and the angle between them is 45◦, can I construct
only one triangle?

Investigation 4-3: Constructing a Triangle Given Two Sides and Included AngleTools Needed: protractor,
pencil, ruler, and paper

1. Draw the longest side (5 in) horizontally, halfway down the page.The drawings in this investigation are to
   scale.


2. At the left endpoint of your line segment, use the protractor to measure a 45◦angle. Mark this measurement.


3. Connect your mark from Step 2 with the left endpoint. Make your line 2 in long, the length of the second side.