You must be well aware of a triangle by now — that it is a 2-dimensional figure with three sides, three angles, and three vertices. Two or more triangles are said to be congruent if their corresponding sides or angles are the same. In other words, Congruent triangles have the same sha...
What are the corresponding parts of congruent triangles? The corresponding parts of congruent triangles are the angles and sides that are congruent, or equally large, between those two triangles. Each side of one triangle is congruent to a side of the other triangle, and each angle in one tria...
Hence, the given triangles are congruent to each other. ΔABC≅ΔEFG AAS (Angle – Angle – Side) CongruenceIt states that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the two triangles are ...
Hypotenuse Leg Theoremis used to prove whether a given set of right triangles are congruent. The Hypotenuse Leg (HL) Theorem states that If the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two right triangles are con...
The RHS (Right Angle-Hypotenuse-Side) congruence rule states that if the hypotenuse and one side of one right triangle is equal to the hypotenuse and corresponding side of the other right triangle, then the two given right triangles are congruent....
SAS Congruence Theorem:When the two sides of a triangle are equal to the two sides of another triangle, and the angles formed by these sides (the included angles) are also equal, then the two triangles are congruent. SAS Similarity Criterion:If two sides of a triangle are proportional with...
Triangle congruence theorem has 5 theorems to prove if a triangle is congruent or not - SSS, SAS, ASA, AAS, and RHS. Learn more about this interesting concept of triangle congruence theorem, the 5 criteria, and solve a few examples.
Let us assume that O is the intersecting point of the diagonals AC and BD. The properties of diagonals of a parallelogram are as follows:The diagonals of a parallelogram bisect each other, i.e., OB = OD and OA = OC. Each diagonal divides the parallelogram into two congruent triangles, ...
The LL theorem, or leg-leg theorem, states that if two right triangles have legs of equal length, then the entire triangles must be congruent. Remember that in this case, the term "leg" refers to the shorter (non-hypotenuse) sides of the triangle. This theorem works because right triangle...
Now it’s time to look at the final postulate for congruent triangles: Hypotenuse-Leg (HL). What is the HL Postulate? The HL Postulate states that if the hypotenuse and leg of oneright triangleare congruent to the hypotenuse and leg of another right triangle, then the two triangles are co...