The pair of triangles that are congruent by ASA is [tex]\boxed{\bf option (d)}[/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.
Option (a)
The first figure shows one side is included between the two angles but the second figure shows two angles and one side as shown in below attachment.
Both the figures don’t have a single property from the above mentioned properties.
Therefore, option (a) is incorrect.
Option (b)
The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by SAS rule not by ASA.
Thus, option (b) is incorrect.
Option (c)
The first figure shows one angle between the two sides and the second figure also shows one angle between the two sides as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by SAS rule not by ASA rule.
Thus, option (c) is incorrect.
Option (d)
The first figure shows two angles and one side is included between them and the second figure shows two angles and one side is included between them as shown in below attachment.
Both have the same property.
Therefore, the triangles are congruent by ASA rule.
Thus, option (d) is correct.
Hence, the [tex]\boxed{\bf option (d)}[/tex] is correct as the triangles are congruent by ASA rule.
Learn more:
1. A problem to determine the equation of line https://brainly.com/question/1646698
2. A problem on ray https://brainly.com/question/1251787
3. A problem to determine intercepts of a line https://brainly.com/question/1332667
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.
