This sentence can be complete as: After a congruence transformation the area of a triangle would be the same as it was before.
Rotation
The two triangle congruence theorems are the AAS(Angle-Angle-Side) and HL(Hypotenuse-Leg) congruence theorems. The AAS congruence theorem states that if two angles and a nonincluded side in one triangle are congruent to two angles and a nonincluded side in another triangle, the two triangles are congruent. In the HL congruence theorem, if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the two triangles are congruent.
There is nothing specific folloing right triangle congruence theorem. It depends on the order in whih the syllabus is taught.
The four congruence theorem for right triangles are:- LL Congruence Theorem --> If the two legs of a right triangle is congruent to the corresponding two legs of another right triangle, then the triangles are congruent.- LA Congruence Theorem --> If a leg and an acute angle of a right triangles is congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.- HA Congruence Theorem --> If the hypotenuse and an acute angle of a right triangle is congruent to the corresponding hypotenuse and acute angle of another triangle, then the triangles are congruent.- HL Congruence Theorem --> If the hypotenuse and a leg of a right triangle is congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.
Since ASA is a congruence postulate and congruence implies similarity, then the answer is : yes.
unchanged
After a congruence transformation, the area of a triangle remains unchanged. Congruence transformations, such as rotations, translations, and reflections, preserve the shape and size of geometric figures. Therefore, while the position or orientation of the triangle may change, its area will stay the same.
It would be left unchanged.
Rotation
The transformation that can verify congruence by sliding one triangle over another is called a translation. During this transformation, one triangle is moved (or "slid") along a straight path without rotating or flipping it, allowing for direct comparison of corresponding sides and angles. If the triangles align perfectly after the translation, it confirms that they are congruent.
The transformation that can verify congruence by sliding one triangle over another is called a translation. During a translation, each point of the triangle moves the same distance in the same direction, ensuring that the shape and size remain unchanged. This means that if one triangle can be translated onto another, they are congruent.
A dilation transformation cannot be used to prove that triangle ABC is congruent to triangle DEF because dilation changes the size of a figure while maintaining its shape. Congruence requires that two figures have the same size and shape, which means all corresponding sides and angles must be equal. Since dilation alters side lengths, it cannot demonstrate congruence, only similarity.
Flipping a triangle over the y-axis is a reflection transformation. This reflection will preserve the triangle's size and shape, ensuring that the resulting triangle is congruent to the original one. By comparing corresponding sides and angles, one can verify that the two triangles are indeed congruent after the reflection.
The two triangle congruence theorems are the AAS(Angle-Angle-Side) and HL(Hypotenuse-Leg) congruence theorems. The AAS congruence theorem states that if two angles and a nonincluded side in one triangle are congruent to two angles and a nonincluded side in another triangle, the two triangles are congruent. In the HL congruence theorem, if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, the two triangles are congruent.
It does not necessarily prove congruence but it does prove similarity. You can have a smaller or bigger triangle that has the same interior angles.
A triangle having 3 congruent sides is an equilateral triangle
The only Two Triangle congruence shortcuts that do not prove congruence are: 1.AAA( Three pairs of angles in a triangle) & 2.ASS or SSA(If the angle is not in between the two sides like ASA.