Respuesta :
ANSWER
The congurence theorem used to prove the triangle are congurent is SAS.
Reason
SAS congurence property
(1) Two pairs of sides of two triangles are equal in length.
(2) The angles included are equal in measurement, then the triangles are congruent.
As given in the question
Two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle.
Thus SAS congurence property is satisfied
Hence proved
The triangles are congruent by [tex]\boxed{\bf Side-Angle-Side\ (SAS)}[/tex].
Further explanation:
Triangles are congruent when all the corresponding sides and interior angles are equal.
There are four theorems by which we say that the triangles are congruent.
1.Side-Side-Side(SSS)
If all the three sides of a triangle are equal to the corresponding sides of the other triangle, then the two triangles are congruent by SSS theorem.
2.Angle-Side-Angle(ASA)
If any two angles and the included side between the angles of one triangle are equal to the corresponding two angles and the included side between the angles of the second triangle then the two triangles are congruent by ASA theorem.
3.Side-Angle-Side(SAS)
If any two sides and angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle then the two triangles are congruent by SAS theorem.
4.Hypotenuse Leg (HL)
If the hypotenuse and side of a right angled triangle is equal to the hypotenuse and a side of the other right angled triangle then the triangles are congruent by HL theorem.
It is given that the two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle.
Option (1)
Here, the option (1) is ASA.
But it is given that there are two sides.
Therefore, option (1) is incorrect.
Option (2)
Here, the option (2) is SSS.
But it is given that there are two sides and one angle.
Therefore, option (2) is incorrect.
Option (3)
Here, the option (3) is SAS.
It is given that there are two sides and one angle between the sides.
By SAS theorem the two triangles are congruent.
Therefore, option (3) is correct.
Option (4)
Here, the option (4) is HL.
But it is given that there are two sides and one angle.
The angle is not specified whether it is right angle or not.
Therefore, option (4) is incorrect.
Learn more:
1. Learn more about the rotation of the triangle about the origin https://brainly.com/question/7437053.
2. Learn more about when a triangle is rotated about the origin https://brainly.com/question/2992432.
3. Learn more about general form of the equation of the circle https://brainly.com/question/1506955
Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Angles and triangles
Keywords: Triangles, angles, sides, congruent triangles, similar triangles, SAS theorem, ASA theorem, SSS theorem, HL theorem, geometry, translation, rotation, reflection, mirror image.
