Indirect Proof

Front

What is an indirect proof?

Back

An indirect proof is a method of proving a statement by assuming the opposite is true and showing that this assumption leads to a contradiction.

Front

What is the principle of congruent triangles?

Back

If two sides of a triangle are congruent, then the angles opposite those sides are also congruent.

Front

What does it mean for angles to be congruent?

Back

Two angles are congruent if they have the same measure.

Front

What is the contradiction in an indirect proof?

Back

A contradiction occurs when the assumption made leads to a conclusion that conflicts with known facts or the original statement.

Front

What is the first step in an indirect proof?

Back

The first step is to assume that the statement you want to prove is false.

Front

What is the significance of the triangle inequality theorem?

Back

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

How do you denote congruent segments?

Back

Congruent segments are denoted using the symbol '≅', for example, AB ≅ DE.

Front

What is the relationship between the sides and angles of a triangle?

Back

In a triangle, larger angles are opposite longer sides, and smaller angles are opposite shorter sides.

Front

What is the definition of a midpoint?

Back

A midpoint is a point that divides a segment into two equal parts.

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if their corresponding sides and angles are equal.