Question

nanoe knight
learn triangle congruence theorems
triangle congruence theorems
sss (side-side-side)
( overline { m n } cong overline { p q } ( 6 ) )
( overline { q r } cong overline { t f } ( 5 ) )
( overline { n r } cong overline { p t } ( 6 ) )
sas (side-angle-side)
asa (angle-side-angle)
aas (angle-angle-side)
hl (hypotenuse-leg)
multiple-choice question
which of the following are the included angles shown in the sas image?
( angle c cong angle f )
( angle b cong angle e )
( angle a cong angle d )

Explanation:

Step1: Recall SAS (Side - Angle - Side)

In the SAS (Side - Angle - Side) congruence criterion, the angle is included between the two sides.

Step2: Analyze the angles in SAS

Looking at the SAS image (the one labeled "SAS (Side - Angle - Side)"), we check which angles are between the marked sides. In a triangle for SAS, the angle that is part of the SAS congruence is the one that has the two sides forming it as the sides given for the SAS condition. For the standard SAS - labeled triangle in geometry (where two sides and the included angle are marked), if we assume the general triangle structure in the given set of images, the included angle is the one that is between the two sides which are used for the "Side - Angle - Side" relation. In the context of triangle congruence for SAS, the included angle is the non - adjacent angle to the non - marked side (when considering the two marked sides). If we consider the typical notation where in a triangle \(ABC\) and \(DEF\) for SAS (\(AB = DE\), \(\angle B=\angle E\), \(BC = EF\)), the included angle is \(\angle B\) (or \(\angle E\) in the congruent triangle).

Answer:

\(\angle B\cong\angle E\)