The SAS Congruence Theorem Practice

Question

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Question
Which of the following triangles are congruent by the SAS Congruence Theorem? Enter the lesser number first.

Triangle #1: a triangle with an angle measuring 60 degrees between sides measuring 3 cm and 6 cm

Triangle #2: A triangle, with the base measuring 3 centimeters and the longest side measuring 6 centimeters. The angle between the base and the longest side measures 60 degrees.

Triangle #3: A triangle, with the base measuring 3 centimeters and the right side measuring 6 centimeters. The angle between the base and the third side, which is on the left side, measures 60 degrees.

(1 point)
Triangle #
and Triangle #
are congruent.

Answer 1

To determine which triangles are congruent by the SAS (Side-Angle-Side) Congruence Theorem, we need to evaluate the given triangles based on the criteria of SAS.

1. Triangle #1 has:

   • Angle: 60 degrees
   • Sides: 3 cm and 6 cm (the angle is between these two sides)

2. Triangle #2 has:

   • Angle: 60 degrees
   • Sides: 3 cm and 6 cm (the angle is between these two sides)

3. Triangle #3 has:

   • Angle: 60 degrees
   • One side (base): 3 cm
   • Other side (right-side): 6 cm
   • The angle is between the base and the third side, but we don't know the length of the third side.

Triangles #1 and #2: Both have the same angle and the same sides (3 cm and 6 cm) where the angle is included, which means they satisfy the SAS condition.

Triangles #1 and #3: The angle is the same, but we do not have the length of the third side in Triangle #3, so we cannot conclude that they are congruent by SAS.

Triangles #2 and #3: While Triangle #2 has sides of 3 cm and 6 cm with the included angle of 60 degrees, we don't know the length of the side opposite the angle in Triangle #3, so they also cannot be concluded as congruent by SAS.

Thus, based on the SAS Congruence Theorem, the only triangles that are congruent by SAS are Triangle #1 and Triangle #2.

So the answer is:

Triangle #1 and Triangle #2 are congruent.