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∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC
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∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to...
If the triangles are congruent then AB=PQ=BC=QR because they are isosceles triangles so PR is also equal to AC. according to SSS congruency. then we find AB=6,BC=6,AC=10.
Perimeter of the triangle=sum of all sides
=6+6+10=22cm. it is your answer.
Perimeter of the triangle=sum of all sides
=6+6+10=22cm. it is your answer.
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∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to...
Given:
- Triangle ABC is an isosceles triangle with AB=BC.
- Triangle ABC is congruent to triangle PQR.
- AB = 6 cm and QR = 10 cm.
To Find:
The perimeter of triangle ABC.
Solution:
To find the perimeter of triangle ABC, we need to find the lengths of sides AB, BC, and AC.
Step 1: Understanding Congruence of Triangles
Congruence of triangles means that two triangles are identical in shape and size. If two triangles are congruent, it means that their corresponding sides and angles are equal.
Step 2: Properties of an Isosceles Triangle
In an isosceles triangle, the two legs (sides opposite to the equal angles) are equal. In triangle ABC, AB = BC.
Step 3: Congruence of Triangles
Triangle ABC is congruent to triangle PQR. This means that the corresponding sides and angles of both triangles are equal.
Step 4: Applying Congruence to Find the Missing Side
Since AB = BC in triangle ABC, it means that QR = RP in triangle PQR. Therefore, RP = 6 cm.
Step 5: Finding the Length of AC
To find the length of AC, we can use the fact that the sum of the lengths of the two congruent sides of an isosceles triangle is greater than the third side.
In triangle ABC, AB = BC = 6 cm. Therefore, AC < 6="" cm="" +="" 6="" cm="12" />
Step 6: Finding the Perimeter
Now that we know the lengths of sides AB, BC, and AC, we can find the perimeter of triangle ABC by summing up the lengths of all three sides.
Perimeter of triangle ABC = AB + BC + AC = 6 cm + 6 cm + AC
Step 7: Final Calculation
To find the perimeter, we need to determine the length of AC.
Since AC < 12="" cm,="" and="" the="" length="" of="" qr="" is="" given="" as="" 10="" cm,="" ac="" must="" be="" less="" than="" 10="" />
Therefore, the perimeter of triangle ABC is 6 cm + 6 cm + AC.
Conclusion:
The perimeter of triangle ABC is 12 cm + AC, where AC is less than 10 cm (as AC < 12="" cm="" and="" qr="10" cm).="" 12="" cm="" and="" qr="10" />
- Triangle ABC is an isosceles triangle with AB=BC.
- Triangle ABC is congruent to triangle PQR.
- AB = 6 cm and QR = 10 cm.
To Find:
The perimeter of triangle ABC.
Solution:
To find the perimeter of triangle ABC, we need to find the lengths of sides AB, BC, and AC.
Step 1: Understanding Congruence of Triangles
Congruence of triangles means that two triangles are identical in shape and size. If two triangles are congruent, it means that their corresponding sides and angles are equal.
Step 2: Properties of an Isosceles Triangle
In an isosceles triangle, the two legs (sides opposite to the equal angles) are equal. In triangle ABC, AB = BC.
Step 3: Congruence of Triangles
Triangle ABC is congruent to triangle PQR. This means that the corresponding sides and angles of both triangles are equal.
Step 4: Applying Congruence to Find the Missing Side
Since AB = BC in triangle ABC, it means that QR = RP in triangle PQR. Therefore, RP = 6 cm.
Step 5: Finding the Length of AC
To find the length of AC, we can use the fact that the sum of the lengths of the two congruent sides of an isosceles triangle is greater than the third side.
In triangle ABC, AB = BC = 6 cm. Therefore, AC < 6="" cm="" +="" 6="" cm="12" />
Step 6: Finding the Perimeter
Now that we know the lengths of sides AB, BC, and AC, we can find the perimeter of triangle ABC by summing up the lengths of all three sides.
Perimeter of triangle ABC = AB + BC + AC = 6 cm + 6 cm + AC
Step 7: Final Calculation
To find the perimeter, we need to determine the length of AC.
Since AC < 12="" cm,="" and="" the="" length="" of="" qr="" is="" given="" as="" 10="" cm,="" ac="" must="" be="" less="" than="" 10="" />
Therefore, the perimeter of triangle ABC is 6 cm + 6 cm + AC.
Conclusion:
The perimeter of triangle ABC is 12 cm + AC, where AC is less than 10 cm (as AC < 12="" cm="" and="" qr="10" cm).="" 12="" cm="" and="" qr="10" />
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∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? 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 ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles?.
∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? 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 ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ∆ABC is an isoscelesangle in which AB=BC.this triangle is congruent to ∆PQR.if AB=6cm,QR=10cm, find perimeter of ∆ABC Related: NCERT Solutions - Congruence of Triangles?.
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