Question

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

Answer 1

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

Answer 2

Answer:

The correct options are 1 and 2.

Step-by-step 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.