Look at the triangles in the diagram.
Determine which of the statements is correct.
We have hundreds of course questions with personalized recommendations + Account 100% premium
Look at the triangles in the diagram.
Determine which of the statements is correct.
Let's consider that:
AC=EF=4
DF=AB=5
Since 5 is greater than 4 and the angle equal to 34 is opposite the larger side in both triangles, the angle ACB must be equal to the angle DEF
Therefore, the triangles are congruent according to the SAS theorem, as a result of this all angles and sides are congruent, and all answers are correct.
All of the above.
Determine whether the triangles DCE and ABE congruent?
If so, according to which congruence theorem?
The included angle is the angle that sits between the two sides you're comparing. In triangle ABC, the 34° angle at C is between sides AC (4) and CB. Match this pattern in the other triangle.
When two triangles are congruent by SAS, they are identical in shape and size. This means all corresponding sides and angles must be equal, not just the ones used to prove congruence.
That's okay! You need to identify corresponding parts. AC corresponds to EF (both equal 4), AB corresponds to DF (both equal 5), and angle C corresponds to angle E (both 34°).
Since the actual side lengths are equal (4 = 4 and 5 = 5), not just proportional, the triangles are congruent, which is stronger than just being similar.
S-A-S means Side-Angle-Side. The angle must be the included angle between the two sides. Think of it as a sandwich: the angle is the filling between two side pieces!
Get unlimited access to all 18 Congruent Triangles questions, detailed video solutions, and personalized progress tracking.
Unlimited Video Solutions
Step-by-step explanations for every problem
Progress Analytics
Track your mastery across all topics
Ad-Free Learning
Focus on math without distractions
No credit card required • Cancel anytime