ashita draw an isosceles triangle with PQ = PR and named it a triangle PQR . she also marked S and t as midpoints of PQ and QR repctivley
1). QT=SE
2). Angle QSR= Angle RTQ
3). QS=RT
WHICH OF THE ABOVE STATEMENT IS TRUE
A . ONLY 3
B. ONLY 1 AND 2
C. ONLY 2 AND 3
D. ALL OPTIONS ARE CORRECT
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Answer:
I apologize for the mistake in my previous response. Let's reevaluate the statements:
1) QT = SE - This statement is true because S and T are the midpoints of PQ and QR, respectively. By the midpoint theorem, the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. Therefore, QT is equal to SE.
2) ∠QSR = ∠RTQ - This statement is true. In an isosceles triangle, the angles opposite the equal sides are congruent. Since PQ = PR, triangle PQR is isosceles, and thus ∠QSR = ∠RTQ.
3) QS = RT - This statement is true. The sides opposite the congruent angles in an isosceles triangle are equal. In this case, since ∠QSR = ∠RTQ, it follows that QS = RT.
Based on the reevaluation:
- Statement 1 is true.
- Statement 2 is true.
- Statement 3 is true.
Therefore, the correct answer is:
D. ALL OPTIONS ARE CORRECT.