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In the isosceles triangle ABC, BA=BC. M and N are points on AC such that MA=MB and NB=NC. Show that triangles AMB and CNB are congruent.?
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In the isosceles triangle ABC, BA=BC. M and N are points on AC such th...
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In the isosceles triangle ABC, BA=BC. M and N are points on AC such th...
Proof:
We are given an isosceles triangle ABC, where BA = BC. Let M and N be points on AC such that MA = MB and NB = NC. We need to prove that triangles AMB and CNB are congruent.
1. Draw a diagram:
Draw an isosceles triangle ABC, where BA = BC. Mark points M and N on AC such that MA = MB and NB = NC.
2. Identify the given information:
- Triangle ABC is an isosceles triangle with BA = BC.
- Points M and N are on AC such that MA = MB and NB = NC.
3. Identify the required information:
We need to prove that triangles AMB and CNB are congruent.
4. Analyze the given information:
Since triangle ABC is isosceles with BA = BC, we know that angle BAC = angle BCA (by definition of an isosceles triangle).
Since MA = MB and NB = NC, we can say that triangles BAM and BCN are congruent by the Side-Angle-Side (SAS) congruence criterion.
5. Use the congruence criterion:
By using the SAS congruence criterion, we can conclude that triangles AMB and CNB are congruent.
6. Conclusion:
Therefore, we have proved that triangles AMB and CNB are congruent.
In summary, we have shown that triangles AMB and CNB are congruent by using the given information and the SAS congruence criterion.
We are given an isosceles triangle ABC, where BA = BC. Let M and N be points on AC such that MA = MB and NB = NC. We need to prove that triangles AMB and CNB are congruent.
1. Draw a diagram:
Draw an isosceles triangle ABC, where BA = BC. Mark points M and N on AC such that MA = MB and NB = NC.
2. Identify the given information:
- Triangle ABC is an isosceles triangle with BA = BC.
- Points M and N are on AC such that MA = MB and NB = NC.
3. Identify the required information:
We need to prove that triangles AMB and CNB are congruent.
4. Analyze the given information:
Since triangle ABC is isosceles with BA = BC, we know that angle BAC = angle BCA (by definition of an isosceles triangle).
Since MA = MB and NB = NC, we can say that triangles BAM and BCN are congruent by the Side-Angle-Side (SAS) congruence criterion.
5. Use the congruence criterion:
By using the SAS congruence criterion, we can conclude that triangles AMB and CNB are congruent.
6. Conclusion:
Therefore, we have proved that triangles AMB and CNB are congruent.
In summary, we have shown that triangles AMB and CNB are congruent by using the given information and the SAS congruence criterion.
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In the isosceles triangle ABC, BA=BC. M and N are points on AC such that MA=MB and NB=NC. Show that triangles AMB and CNB are congruent.?
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In the isosceles triangle ABC, BA=BC. M and N are points on AC such that MA=MB and NB=NC. Show that triangles AMB and CNB are congruent.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In the isosceles triangle ABC, BA=BC. M and N are points on AC such that MA=MB and NB=NC. Show that triangles AMB and CNB are congruent.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the isosceles triangle ABC, BA=BC. M and N are points on AC such that MA=MB and NB=NC. Show that triangles AMB and CNB are congruent.?.
In the isosceles triangle ABC, BA=BC. M and N are points on AC such that MA=MB and NB=NC. Show that triangles AMB and CNB are congruent.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In the isosceles triangle ABC, BA=BC. M and N are points on AC such that MA=MB and NB=NC. Show that triangles AMB and CNB are congruent.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the isosceles triangle ABC, BA=BC. M and N are points on AC such that MA=MB and NB=NC. Show that triangles AMB and CNB are congruent.?.
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