The SAS Congruence Theorem Quick Check
2 of 52 of 5 Items
Question
Which of the following pairs of triangles could you use to justify that the SAS Congruence Theorem is true?(1 point)
Responses
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E F is congruent to side H I. Angle F is congruent to angle I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E F is congruent to side H I. Angle F is congruent to angle I. Angle E is congruent to angle H.
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E G is congruent to side H J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E G is congruent to side H J. Side E F is congruent to side H I. Angle E is congruent to angle H.
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I. Angle E is congruent to angle H.
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I.
The SAS Congruence Theorem Quick Check
2 of 52 of 5 Items
Question
Which of the following pairs of triangles could you use to justify that the SAS Congruence Theorem is true?(1 point)
Responses
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E F is congruent to side H I. Angle F is congruent to angle I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E F is congruent to side H I. Angle F is congruent to angle I. Angle E is congruent to angle H.
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E G is congruent to side H J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side E G is congruent to side H J. Side E F is congruent to side H I. Angle E is congruent to angle H.
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I. Angle E is congruent to angle H.
Image with alt text: An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I. Angle E is congruent to angle H.
An illustration shows two triangles side by side. The two triangles are labeled E F G and H I J. Side F G is congruent to side I J. Side E F is congruent to side H I.
2 answers
To justify that the SAS (Side-Angle-Side) Congruence Theorem is true, you need two sides of one triangle that are congruent to two sides of another triangle, and the angle included between those two sides must also be congruent.
Looking at the options provided:
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First Option: Side \(EF\) is congruent to side \(HI\), and angles \(F\) and \(I\), and angles \(E\) and \(H\) are congruent. This does not use the SAS criteria effectively because it doesn't include the angle between the two sides.
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Second Option: Side \(EG\) is congruent to side \(HJ\), side \(EF\) is congruent to side \(HI\), and angle \(E\) is congruent to angle \(H\). This does not fulfill the SAS requirement either, as the angle included between the two sides is not mentioned.
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Third Option: Side \(FG\) is congruent to side \(IJ\), side \(EF\) is congruent to side \(HI\), and angle \(E\) is congruent to angle \(H\). This also does not work, because angle \(E\) is not between the two sides mentioned.
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Fourth Option: Side \(FG\) is congruent to side \(IJ\), and side \(EF\) is congruent to side \(HI\), but it fails to specify an angle.
None of the options clearly meet the SAS criteria; however, the second option comes closest to using two sides and an included angle, which are necessary to apply the SAS theorem.
Conclusion: In theory, the second option is the most likely candidate, assuming angle E is the angle between the two sides mentioned. Please verify the arrangement of the triangles with respect to the angles to make sure it fits the definition correctly.
1 answer