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

The correct options are;

mQRT

mQRT mSRT

Step-by-step explanation:

Given information;

The triangle QST is isosceles with QT ≅ ST.

The angle STR ans RTQ are congruent.

Now, consider two triangles QTR and STR

In the following triangle

1. TR  ≅  TR (having reflective property)

2. QTR ≅ STR (as given in question)

3. QT ≅ ST (as given in information)

Now, according to SAS postulate , two congruent triangle have congruent corresponding to their sides ,

Hence ,

1. QR ≅ SR

2. QRT ≅ SRT

Since, this above two angles are congruent they will have same measure

That will be

Hence, The correct options are;

mQRT

mQRT mSRT

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m∠QRT = 90°

m∠QRT = m∠SRT

Step-by-step explanation:

Triangle QST is isosceles with QT ≅ ST. In isoscels triangle QST, angles STR and RTQ are congruent.

RT is angle T bisector, so angles QTR and STR are congruent.

Consider two triangles QTR and STR. In these triangles:

By SAS postulate, these two triangles are congruent. Two congruent triangles have congruent corresponding sides, so

Angles QRT and SRT are supplementary (add up to 180°). Since these two angles are congruent, they have the same measure equal to

So, true options are

m∠QRT = 90°

m∠QRT = m∠SRT

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