What you’ll learn
Use SAS.
Key idea
SAS needs the angle between the paired sides; corresponding triangle parts match after congruence.
Worked example
Enter the exact value or ordered values in the format requested below.
Triangles ABC and DEF have AB=AC=DE=DF=4, with A-D, B-E, C-F correspondence. Included angles A=D=40 degrees; B=70 degrees. Use SAS to find E in degrees.
- Equal legs meet at A and D; matching included angles 40 degrees establish SAS.
- The realizable isosceles triangles have base angles (180-40)/2=70; corresponding E equals B.
Answer: 70
Quick Check
Evaluate a worked attempt at use sas, identify the first invalid step, and provide the correction.
Triangles ABC and DEF have AB=AC=DE=DF=7, with A-D, B-E, C-F correspondence. Instead, only nonincluded B=E=40 degrees are stated. Student Step 1 notes two side and one angle pairs match; Step 2 says these are directly the SAS data. Identify first invalid step and state the directly required angle location, without ruling out other possible congruence reasoning.