Topic 4: Triangle Congruence

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and its length is half the length of that side.

Front

What is the Triangle Congruence Postulate?

Back

The Triangle Congruence Postulate states that if two triangles have two sides and the included angle equal to two sides and the included angle of another triangle, then the triangles are congruent (SAS).

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, which is a criterion for triangle congruence stating that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the significance of corresponding angles in parallel lines?

Back

Corresponding angles are equal when a transversal crosses two parallel lines, which is a key concept in proving triangles congruent.

Front

What is the definition of vertical angles?

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always equal.

Front

What is the purpose of a proof in geometry?

Back

A proof is a logical argument that uses definitions, properties, and previously proven statements to demonstrate the truth of a geometric statement.

Front

What does the term 'congruent' mean in geometry?

Back

Congruent means that two figures have the same shape and size, and can be superimposed on each other.

Front

What is the relationship between the angles in a triangle?

Back

The sum of the interior angles in a triangle is always 180 degrees.

Front

What is the definition of alternate interior angles?

Back

Alternate interior angles are pairs of angles that are on opposite sides of a transversal and inside the two lines. If the lines are parallel, these angles are equal.

Front

What is the definition of the Side-Angle-Side (SAS) congruence criterion?

Back

The SAS criterion states that if two sides of one triangle are equal to two sides of another triangle, and the included angle is also equal, then the triangles are congruent.