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A children's park is in the shape of isosceles triangle said PQR with PQ = PR, S and T are points on QR such that QT = RS. Name the type of ∆PST?
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A children's park is in the shape of isosceles triangle said PQR with ...
Type of Triangle PST
To determine the type of triangle PST, we start by analyzing the properties of triangle PQR and the points S and T on side QR.
Properties of Isosceles Triangle PQR
- Triangle PQR is isosceles, meaning PQ = PR.
- The angles at the base (Q and R) are equal, i.e., ∠PQR = ∠PRQ.
Understanding Points S and T
- Points S and T are located on side QR such that QT = RS.
- This equality of segments indicates that QT and RS are of equal length.
Analyzing Triangle PST
- Since QT = RS, and both T and S are on line QR, triangle PST has two sides that are equal in length.
- Specifically, PS is a common side for both segments, and the segments QT and RS are equal.
Conclusion
- The property of having two equal sides in triangle PST (PS = PS and QT = RS) establishes that triangle PST is **isosceles**.
- Therefore, triangle PST is an isosceles triangle due to the equality of the segments QT and RS.
In summary, triangle PST is isosceles because it has two sides that are equal in length, consistent with the properties of triangle PQR and the given conditions with points S and T.
To determine the type of triangle PST, we start by analyzing the properties of triangle PQR and the points S and T on side QR.
Properties of Isosceles Triangle PQR
- Triangle PQR is isosceles, meaning PQ = PR.
- The angles at the base (Q and R) are equal, i.e., ∠PQR = ∠PRQ.
Understanding Points S and T
- Points S and T are located on side QR such that QT = RS.
- This equality of segments indicates that QT and RS are of equal length.
Analyzing Triangle PST
- Since QT = RS, and both T and S are on line QR, triangle PST has two sides that are equal in length.
- Specifically, PS is a common side for both segments, and the segments QT and RS are equal.
Conclusion
- The property of having two equal sides in triangle PST (PS = PS and QT = RS) establishes that triangle PST is **isosceles**.
- Therefore, triangle PST is an isosceles triangle due to the equality of the segments QT and RS.
In summary, triangle PST is isosceles because it has two sides that are equal in length, consistent with the properties of triangle PQR and the given conditions with points S and T.
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A children's park is in the shape of isosceles triangle said PQR with PQ = PR, S and T are points on QR such that QT = RS. Name the type of ∆PST?
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A children's park is in the shape of isosceles triangle said PQR with PQ = PR, S and T are points on QR such that QT = RS. Name the type of ∆PST? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A children's park is in the shape of isosceles triangle said PQR with PQ = PR, S and T are points on QR such that QT = RS. Name the type of ∆PST? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A children's park is in the shape of isosceles triangle said PQR with PQ = PR, S and T are points on QR such that QT = RS. Name the type of ∆PST?.
A children's park is in the shape of isosceles triangle said PQR with PQ = PR, S and T are points on QR such that QT = RS. Name the type of ∆PST? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A children's park is in the shape of isosceles triangle said PQR with PQ = PR, S and T are points on QR such that QT = RS. Name the type of ∆PST? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A children's park is in the shape of isosceles triangle said PQR with PQ = PR, S and T are points on QR such that QT = RS. Name the type of ∆PST?.
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