Congruent Triangles
Congruent triangles are two or more triangles that have the same size and shape
Congruent triangles are two or more triangles that have the same size and shape. When two triangles are congruent, it means that all corresponding sides and angles of the triangles are equal.
To determine if two triangles are congruent, we use several methods such as side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and hypotenuse-leg (HL).
1. Side-Side-Side (SSS):
If the lengths of the three sides of one triangle are equal to the lengths of the corresponding three sides of another triangle, then the two triangles are congruent.
2. Side-Angle-Side (SAS):
If two sides of one triangle are equal to two sides of another triangle, and the included angle between those sides are also equal, then the two triangles are congruent.
3. Angle-Side-Angle (ASA):
If two angles of one triangle are equal to two angles of another triangle, and the included side between those angles are also equal, then the two triangles are congruent.
4. Angle-Angle-Side (AAS):
If two angles of one triangle are equal to two angles of another triangle, and one side between those angles are equal, then the two triangles are congruent.
5. Hypotenuse-Leg (HL) (specific to right triangles only):
If the hypotenuse and leg of one right triangle are equal to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
Once we prove that two triangles are congruent, we can use the congruence statement to show that corresponding parts of the triangles are equal. For example, if triangles ABC and DEF are congruent, we can say that angle A = angle D, side AB = side DE, angle B = angle E, side BC = side EF, angle C = angle F, and side AC = side DF.
It is important to note that congruence is a symmetric relation, which means that if triangle ABC is congruent to triangle DEF, then triangle DEF is also congruent to triangle ABC.
More Answers:
Unveiling the Rhombus Corollary: Exploring the Geometric Properties and Applications of RhombusesThe Rectangle Corollary: Identifying Rectangles by Congruent Opposite Sides
Understanding Similar Triangles: Properties, Methods, and Applications for Solving Real-World Problems