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

Question

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 look for triangles that have two sides of equal length and the included angle between those sides also equal.

Let's analyze the triangles:

Triangle #1:

• Side 1: 3 cm
• Side 2: 6 cm
• Included angle: 60 degrees

Triangle #2:

• Side (base): 3 cm
• Longest side: 6 cm
• Included angle: 60 degrees (angle between the base and the longest side)

In Triangle #1 and Triangle #2:

• Both have sides of 3 cm and 6 cm with an included angle of 60 degrees, which makes them congruent by the SAS theorem.

Triangle #3:

• Base: 3 cm
• Side 2: 6 cm
• Angle between base and left side: 60 degrees

Now, Triangle #3 has a 3 cm side and a 6 cm side, with the included angle being 60 degrees between them. Thus, Triangle #1 and Triangle #3 are also congruent by the SAS theorem.

In conclusion:

• Triangle #1 and Triangle #2 are congruent.
• Triangle #1 and Triangle #3 are also congruent.

However, only Triangle #1 and Triangle #2 mention specific angles and sides confirming they satisfy the SAS criteria directly with the provided angles.

Therefore, the final answer is: Triangle #1 and Triangle #2 are congruent.