02 Triangle Congruency

Front

What is Triangle Congruency?

Back

Triangle congruency refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

Front

What are the criteria for triangle congruency?

Back

The main criteria for triangle congruency are: 1. Side-Side-Side (SSS) - All three sides of one triangle are equal to the three sides of another triangle. 2. Side-Angle-Side (SAS) - Two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle. 3. Angle-Side-Angle (ASA) - Two angles and the included side of one triangle are equal to two angles and the included side of another triangle. 4. Angle-Angle-Side (AAS) - Two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle. 5. Hypotenuse-Leg (HL) - In right triangles, the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle.

Front

If ∆ABC≅∆XYZ, what can we conclude about the sides?

Back

If ∆ABC≅∆XYZ, then AB≅XY, AC≅XZ, and BC≅YZ.

Front

What does the notation ∆EHG≅∆KFC signify?

Back

The notation ∆EHG≅∆KFC signifies that triangle EHG is congruent to triangle KFC, meaning their corresponding sides and angles are equal.

Front

How do you find the value of x in a triangle?

Back

To find the value of x in a triangle, you can use the properties of triangle congruency, the Pythagorean theorem, or the sum of angles in a triangle, depending on the information given.

Front

What is the sum of the interior angles of a triangle?

Back

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

Front

If two triangles are congruent, what can be said about their corresponding angles?

Back

If two triangles are congruent, their corresponding angles are equal.

Front

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

Back

The SAS criterion is significant because it allows us to prove that two triangles are congruent if we know two sides and the angle between them are equal.

Front

What is the Angle-Side-Angle (ASA) 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.

Front

What is the Hypotenuse-Leg (HL) criterion?

Back

The HL criterion applies to right triangles and states that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.