To determine which pair of triangles can be proven congruent using the Side-Angle-Side (SAS) theorem, we need to check for:
Two pairs of corresponding sides that are equal.
The included angle (the angle between the two given sides) that is also equal.
Now, let’s analyze each option in the image:
Top-left: Shows a triangle with two sides marked and an angle between them. This could be a candidate for SAS.
Top-right: Two triangles are given, but they only show sides, not an included angle. So, they don’t satisfy SAS.
Bottom-left: A large triangle with a right angle and two marked sides. The right angle is the included angle between the sides, so this could be SAS.
Bottom-right: A quadrilateral split into two triangles with equal sides marked. However, without a clearly marked included angle, SAS cannot be confirmed.
Answer:
The bottom-left and top-left pairs of triangles can be proven congruent using SAS because they have two pairs of equal sides and a clearly marked included angle.
