Triangle QST is isosceles, and Line segment R T bisects AngleT.
Triangle Q S T is cut by bisector R T. The lengths of sides S T and Q T are congruent. Line segments S R and R Q are congruent. Angles S T R and R T Q are congruent.
What is true about AngleQRT? Select two options.
Measure of angleQRT = 90°
Measure of angleQRT = Measure of angleSRT
AngleQRT Is-congruent-to AngleSTQ
Measure of angleQRT = 2*Measure of angleRTQ
AngleQRT Is-congruent-to AngleRTQ
Answers
Answer:
Option (A) and (B) are true.
Step-by-step explanation:
Given: ΔQST is an isosceles triangle such that ST = QT.
The line segment RT bisects ∠T, i.e.,
∠RTQ = ∠STR and SR = RQ.
In ΔSTR and ΔRTQ,
ST = QT (Given)
TR = TR (Common side)
SR = RQ (Given)
By SSS congruence rule, ΔSTR ≅ ΔRTQ
Thus, ∠QRT = ∠SRT (By CPCT)
(A) ∠QRT = 90°
Since ∠QRT = ∠SRT . . . . . (i)
On a line segment SRQ,
∠QRT + ∠SRT = 180° (Sum of linear pair is 180°)
∠QRT + ∠QRT = 180°
2∠QRT = 180°
∠QRT = 90°
Thus, option (A) is true.
(B) Yes, the ∠QRT = ∠SRT (By CPCT)
Thus, option (B) is true.
(C) ∠QRT ≅ ∠STQ
Since ∠QRT = 90°.
Also, ΔQST is an isosceles triangle, So, ∠STQ ≠ 90°.
Thus, option C) is not true.
(D) ∠QRT = 2∠RTQ
Let suppose 2∠RTQ ≅ ∠QRT.
⇒ 2∠RTQ = 90° (Since ∠QRT = 90°)
⇒ ∠RTQ = 45°
⇒ ∠RQT = 45° (Angle sum property)
By property, sides opposite to equals angles are equal, i.e.,
RT = RQ (Not possible)
Thus, Option (D) is not true.
(E) ∠QRT ≅ ∠RTQ
In a triangle, two angles cannot of 90°.
Thus, option (E) is not true.
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Answer:
AB
Step-by-step explanation:
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