5.23: Congruent Triangles BW

Front

What does it mean for two triangles to be congruent?

Back

Two triangles are congruent if they have the same size and shape, meaning all corresponding sides and angles are equal.

Front

If ∆XYZ ≅ ∆KLM, what can be said about the corresponding angles?

Back

If ∆XYZ ≅ ∆KLM, then ∠Y ≅ ∠L, ∠Z ≅ ∠M, and ∠X ≅ ∠K.

Front

What is the Corresponding Parts of Congruent Triangles (CPCTC) theorem?

Back

The CPCTC theorem states that if two triangles are congruent, then their corresponding parts (sides and angles) are also congruent.

Front

How do you determine which sides correspond in congruent triangles?

Back

To determine which sides correspond in congruent triangles, you can use the order of the vertices in the congruence statement (e.g., in ∆XYZ ≅ ∆TRS, XY corresponds to TR).

Front

What is the significance of the symbol '≅' in geometry?

Back

The symbol '≅' indicates that two geometric figures are congruent.

Front

What is the sum of the interior angles in any triangle?

Back

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

Front

If one angle of a triangle measures 90 degrees, what type of triangle is it?

Back

If one angle of a triangle measures 90 degrees, it is a right triangle.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides (Pythagorean theorem).

Front

How can you prove that two triangles are congruent?

Back

Two triangles can be proven congruent using several methods: Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), or Hypotenuse-Leg (HL) for right triangles.

Front

What is the Angle-Side-Angle (ASA) congruence criterion?

Back

The ASA criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.