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In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether the triangles are congruent to each other or not:
- a)Yes, by ASA Congruence theorem they are congruent
- b)Yes, by SAS Congruence theorem they are congruent
- c)No, they are not congruent
- d)Yes, by SSS Congruence theorem they are congruent
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether t...
Let's analyze the given information step by step to determine whether triangles ΔABC and ΔPBC are congruent.
- Given:
- AB = BP
- AC = PC
- BC = BC (common side)
- Triangles Involved:
- ΔABC with sides AB, BC, and AC.
- ΔPBC with sides PB (which is equal to AB), BC, and PC (which is equal to AC).
- Corresponding Sides:
- AB corresponds to BP
- AC corresponds to PC
- BC corresponds to BC
- Applying the SSS Congruence Theorem:The Side-Side-Side (SSS) Congruence Theorem states that if all three corresponding sides of two triangles are equal in length, then the triangles are congruent.
- AB = BP (First pair of corresponding sides)
- AC = PC (Second pair of corresponding sides)
- BC = BC (Third pair of corresponding sides, common side)
Since all three pairs of corresponding sides are equal, ΔABC ≅ ΔPBC by the SSS Congruence Theorem.
Most Upvoted Answer
In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether t...
Given that AB = BP and AC = PC, we need to determine whether triangles ABC and PBC are congruent or not. Let's analyze the options one by one.
a) Yes, by ASA Congruence theorem they are congruent.
According to the ASA (Angle-Side-Angle) Congruence theorem, two triangles are congruent if they have two corresponding angles and the included side equal. However, in this case, we only know that the corresponding sides are equal, but we don't have any information about the angles. Therefore, we cannot conclude that the triangles are congruent using the ASA Congruence theorem.
b) Yes, by SAS Congruence theorem they are congruent.
According to the SAS (Side-Angle-Side) Congruence theorem, two triangles are congruent if they have two corresponding sides and the included angle equal. In this case, we have AB = BP and AC = PC, which are the corresponding sides, but we don't have any information about the included angle. Therefore, we cannot conclude that the triangles are congruent using the SAS Congruence theorem.
c) No, they are not congruent.
This option suggests that the triangles are not congruent without providing any reasoning. We cannot simply say that the triangles are not congruent without any valid justification.
d) Yes, by SSS Congruence theorem they are congruent.
According to the SSS (Side-Side-Side) Congruence theorem, two triangles are congruent if they have three corresponding sides equal. In this case, we have AB = BP and AC = PC, which are the corresponding sides. Additionally, we know that BC = BC since it is a common side. Therefore, all three corresponding sides of the triangles are equal, satisfying the condition for congruence by the SSS Congruence theorem. Hence, we can conclude that the triangles ABC and PBC are congruent.
In conclusion, the correct answer is option 'd'. The triangles ABC and PBC are congruent by the SSS Congruence theorem as all three corresponding sides are equal.
a) Yes, by ASA Congruence theorem they are congruent.
According to the ASA (Angle-Side-Angle) Congruence theorem, two triangles are congruent if they have two corresponding angles and the included side equal. However, in this case, we only know that the corresponding sides are equal, but we don't have any information about the angles. Therefore, we cannot conclude that the triangles are congruent using the ASA Congruence theorem.
b) Yes, by SAS Congruence theorem they are congruent.
According to the SAS (Side-Angle-Side) Congruence theorem, two triangles are congruent if they have two corresponding sides and the included angle equal. In this case, we have AB = BP and AC = PC, which are the corresponding sides, but we don't have any information about the included angle. Therefore, we cannot conclude that the triangles are congruent using the SAS Congruence theorem.
c) No, they are not congruent.
This option suggests that the triangles are not congruent without providing any reasoning. We cannot simply say that the triangles are not congruent without any valid justification.
d) Yes, by SSS Congruence theorem they are congruent.
According to the SSS (Side-Side-Side) Congruence theorem, two triangles are congruent if they have three corresponding sides equal. In this case, we have AB = BP and AC = PC, which are the corresponding sides. Additionally, we know that BC = BC since it is a common side. Therefore, all three corresponding sides of the triangles are equal, satisfying the condition for congruence by the SSS Congruence theorem. Hence, we can conclude that the triangles ABC and PBC are congruent.
In conclusion, the correct answer is option 'd'. The triangles ABC and PBC are congruent by the SSS Congruence theorem as all three corresponding sides are equal.
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In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether t...
BC = BC ( common )AB = BP ( given )AC = PC ( given )Therefore , by sss triangle ABC congruent to trianglePBC
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In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether the triangles are congruent to each other or not:a)Yes, by ASA Congruence theorem they are congruentb)Yes, by SAS Congruence theorem they are congruentc)No, they are not congruentd)Yes, by SSS Congruence theorem they are congruentCorrect answer is option 'D'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether the triangles are congruent to each other or not:a)Yes, by ASA Congruence theorem they are congruentb)Yes, by SAS Congruence theorem they are congruentc)No, they are not congruentd)Yes, by SSS Congruence theorem they are congruentCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether the triangles are congruent to each other or not:a)Yes, by ASA Congruence theorem they are congruentb)Yes, by SAS Congruence theorem they are congruentc)No, they are not congruentd)Yes, by SSS Congruence theorem they are congruentCorrect answer is option 'D'. Can you explain this answer?.
In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether the triangles are congruent to each other or not:a)Yes, by ASA Congruence theorem they are congruentb)Yes, by SAS Congruence theorem they are congruentc)No, they are not congruentd)Yes, by SSS Congruence theorem they are congruentCorrect answer is option 'D'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether the triangles are congruent to each other or not:a)Yes, by ASA Congruence theorem they are congruentb)Yes, by SAS Congruence theorem they are congruentc)No, they are not congruentd)Yes, by SSS Congruence theorem they are congruentCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In ΔABC and ΔPBC, AB = BP and AC = PC. Can you say whether the triangles are congruent to each other or not:a)Yes, by ASA Congruence theorem they are congruentb)Yes, by SAS Congruence theorem they are congruentc)No, they are not congruentd)Yes, by SSS Congruence theorem they are congruentCorrect answer is option 'D'. Can you explain this answer?.
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