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in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA
? Related: SSS Condition for Congruence
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in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Re...
**SSS Condition for Congruence**
The SSS condition for congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In other words, if the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent.
**Given Information**
In Figure 9.9, it is given that AB = CD and AD = BC. We need to prove that triangle ADC is similar to triangle CBA.
**Proof**
To prove that triangle ADC is similar to triangle CBA, we need to show that their corresponding sides are proportional and their corresponding angles are congruent.
**Corresponding Sides**
In this case, we have the following corresponding sides:
- AD corresponds to CB
- DC corresponds to AB
- AC corresponds to CA (common side)
We are given that AB = CD and AD = BC. From this information, we can see that the corresponding sides are equal in length.
**Corresponding Angles**
To show that the corresponding angles are congruent, we can use the fact that opposite sides in a parallelogram are parallel. Since AB is parallel to CD and AD is parallel to BC, we can conclude that angle ADC is congruent to angle CBA, and angle CDA is congruent to angle BAC.
**Conclusion**
Since the corresponding sides of triangle ADC and triangle CBA are equal in length, and their corresponding angles are congruent, we can conclude that triangle ADC is similar to triangle CBA based on the SSS condition for congruence.
Therefore, we have proved that triangle ADC is similar to triangle CBA.
The SSS condition for congruence states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent. In other words, if the lengths of the corresponding sides of two triangles are equal, then the triangles are congruent.
**Given Information**
In Figure 9.9, it is given that AB = CD and AD = BC. We need to prove that triangle ADC is similar to triangle CBA.
**Proof**
To prove that triangle ADC is similar to triangle CBA, we need to show that their corresponding sides are proportional and their corresponding angles are congruent.
**Corresponding Sides**
In this case, we have the following corresponding sides:
- AD corresponds to CB
- DC corresponds to AB
- AC corresponds to CA (common side)
We are given that AB = CD and AD = BC. From this information, we can see that the corresponding sides are equal in length.
**Corresponding Angles**
To show that the corresponding angles are congruent, we can use the fact that opposite sides in a parallelogram are parallel. Since AB is parallel to CD and AD is parallel to BC, we can conclude that angle ADC is congruent to angle CBA, and angle CDA is congruent to angle BAC.
**Conclusion**
Since the corresponding sides of triangle ADC and triangle CBA are equal in length, and their corresponding angles are congruent, we can conclude that triangle ADC is similar to triangle CBA based on the SSS condition for congruence.
Therefore, we have proved that triangle ADC is similar to triangle CBA.
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in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence?
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in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence?.
in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in figure 9.9 it is given that AB=CD and AD=BC prove that ∆ADC≈∆CBA Related: SSS Condition for Congruence?.
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