Triangle Congruence: SAS Criterion

The video tutorial explains the concept of included angles in geometry, focusing on their role in determining triangle congruence. It covers the Side-Side-Side (SSS) and Side-Angle-Side (SAS) congruence criteria, emphasizing the importance of the angle being included between two sides. The tutorial also addresses common mistakes made when identifying SAS congruence and highlights the necessity of correctly identifying included angles for accurate congruence statements.

What is an included angle?

• An angle that is between two sides of a triangle

• An angle that is not part of the triangle

• An angle that is outside the triangle

• An angle that is equal to 90 degrees

Why is the concept of an included angle important?

• It helps in determining the area of a triangle

• It is crucial for understanding triangle congruence

• It is necessary for finding the height of a triangle

• It is used to calculate the perimeter of a triangle

What does the Side-Side-Side (SSS) congruence criterion state?

• If two triangles have two equal angles, they are congruent

• If two triangles have one equal side, they are congruent

• If two triangles have the same side lengths, they are congruent

• If two triangles have the same angles, they are congruent

In the context of triangle congruence, what does SAS stand for?

• Side-Angle-Side-Angle

• Side-Angle-Angle

• Side-Angle-Side

• Side-Side-Angle

For the SAS criterion, where must the angle be located?

• At the top of the triangle

• Outside the triangle

• At the base of the triangle

• Between the two sides

What is a common mistake when identifying included angles?

• Using the wrong units for the angle

• Confusing the angle with a side

• Placing the angle outside the triangle

• Not ensuring the angle is between the two sides

Why is it incorrect to skip over a side when identifying an included angle?

• It makes the triangle larger

• It results in an incorrect congruence statement

• It changes the shape of the triangle

• It alters the angle measurement

What must be true for two triangles to be congruent under the SAS criterion?

• They must have the same perimeter

• They must have equal angles only

• They must have equal side lengths and the included angle

• They must have the same area

What is the significance of the included angle in the SAS criterion?

• It helps in calculating the area

• It determines the height of the triangle

• It ensures the triangles are similar

• It is crucial for establishing congruence

What happens if the angle is not included between the two sides in SAS?

• The triangles become scalene

• The triangles become isosceles

• The triangles are not congruent

• The triangles are still congruent