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Triangle QST is isosceles, and bisects T.

What is true about QRT? Check all that apply.

QRT = 90°
QRT = SRT
QRT STQ
QRT = 2*RTQ
QRT RTQ

Triangle QST is isosceles, and bisects T. What is true about QRT? Check all that apply-example-1
User JLDiaz
by
7.4k points

2 Answers

2 votes

Answer:

The correct options are 1 and 2.

Explanation:

Given information: Triangle QST is isosceles, and bisects T.

In triangle QRT and SRT,


TR=TR (common side)


\angle STR=\angle QTR (Bisector)


TQ=TS (Isosceles triangle)

By SAS rule,


\triangle STR\cong \triangle QTR


QRT=SRT (CPCTC)

Bisector of an isosceles triangle is the altitude of triangle.


\angle QRT=90^(\circ)

Therefore options 1 and 2 are correct.

User Jordan Schnur
by
8.0k points
3 votes

Answer;

  • QRT = 90°
  • QRT = SRT

Explanation;

  • An isosceles triangle is a type of triangle which has two sides equal, the base angles of this triangle are also equal or congruent.
  • From the Isosceles triangle theorem, the perpendicular bisector of the base of an isosceles triangle also bisects the vertex angle. Thus, SR = RQ and ∠STR = ∠QTR .
  • Thus; angle QRT is right angled, as TR acts as a perpendicular bisector of the base. Also SRT =QRT
User Olkunmustafa
by
8.6k points
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