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PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=angle q and angler=angle s?
Most Upvoted Answer
PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=a...
If the opposite sides are parallel .. and then the angle P= Q
AND
ANGLE R = S.
AND
ANGLE R = S.
Community Answer
PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=a...
Proof:
To prove that angle P = angle Q and angle R = angle S, we can use the properties of parallel lines and transversals.
Given: PQ || RS and PS = QR
Proof of angle P = angle Q:
1. Since PQ || RS, we can say that angle PQS and angle QRS are corresponding angles.
2. Corresponding angles are congruent when the lines are parallel.
3. Therefore, angle PQS = angle QRS.
4. Since PS = QR, we can also say that angle QPS = angle QRP by vertically opposite angles theorem.
5. Now, we have angle PQS = angle QRS and angle QPS = angle QRP.
6. By adding these two equations, we get angle PQS + angle QPS = angle QRS + angle QRP.
7. Simplifying the equation, we get angle PQS + angle QPS = angle QRP + angle QRS.
8. Rearranging the terms, we get angle P + angle Q = angle R + angle S.
9. Since angle PQS = angle QRS, we can substitute angle P + angle Q with angle R + angle S.
10. Therefore, angle P + angle Q = angle R + angle S becomes angle R + angle S = angle R + angle S.
11. This implies that angle P = angle Q.
Proof of angle R = angle S:
1. Since PQ || RS, we can say that angle PSQ and angle QSR are corresponding angles.
2. Corresponding angles are congruent when the lines are parallel.
3. Therefore, angle PSQ = angle QSR.
4. Since PS = QR, we can also say that angle SPQ = angle SRQ by vertically opposite angles theorem.
5. Now, we have angle PSQ = angle QSR and angle SPQ = angle SRQ.
6. By adding these two equations, we get angle PSQ + angle SPQ = angle QSR + angle SRQ.
7. Simplifying the equation, we get angle PSQ + angle SPQ = angle SRQ + angle QSR.
8. Rearranging the terms, we get angle R + angle S = angle R + angle S.
9. This implies that angle R = angle S.
Therefore, we have proved that angle P = angle Q and angle R = angle S using the given conditions and properties of parallel lines and transversals.
To prove that angle P = angle Q and angle R = angle S, we can use the properties of parallel lines and transversals.
Given: PQ || RS and PS = QR
Proof of angle P = angle Q:
1. Since PQ || RS, we can say that angle PQS and angle QRS are corresponding angles.
2. Corresponding angles are congruent when the lines are parallel.
3. Therefore, angle PQS = angle QRS.
4. Since PS = QR, we can also say that angle QPS = angle QRP by vertically opposite angles theorem.
5. Now, we have angle PQS = angle QRS and angle QPS = angle QRP.
6. By adding these two equations, we get angle PQS + angle QPS = angle QRS + angle QRP.
7. Simplifying the equation, we get angle PQS + angle QPS = angle QRP + angle QRS.
8. Rearranging the terms, we get angle P + angle Q = angle R + angle S.
9. Since angle PQS = angle QRS, we can substitute angle P + angle Q with angle R + angle S.
10. Therefore, angle P + angle Q = angle R + angle S becomes angle R + angle S = angle R + angle S.
11. This implies that angle P = angle Q.
Proof of angle R = angle S:
1. Since PQ || RS, we can say that angle PSQ and angle QSR are corresponding angles.
2. Corresponding angles are congruent when the lines are parallel.
3. Therefore, angle PSQ = angle QSR.
4. Since PS = QR, we can also say that angle SPQ = angle SRQ by vertically opposite angles theorem.
5. Now, we have angle PSQ = angle QSR and angle SPQ = angle SRQ.
6. By adding these two equations, we get angle PSQ + angle SPQ = angle QSR + angle SRQ.
7. Simplifying the equation, we get angle PSQ + angle SPQ = angle SRQ + angle QSR.
8. Rearranging the terms, we get angle R + angle S = angle R + angle S.
9. This implies that angle R = angle S.
Therefore, we have proved that angle P = angle Q and angle R = angle S using the given conditions and properties of parallel lines and transversals.
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PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=angle q and angler=angle s?
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PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=angle q and angler=angle s? 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 PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=angle q and angler=angle s? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=angle q and angler=angle s?.
PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=angle q and angler=angle s? 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 PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=angle q and angler=angle s? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for PQRS is a quadrilateral in which PQ||RS and Ps=QR prove that angle p=angle q and angler=angle s?.
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