Question

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

Answer 1

Answer:

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:

• TR ≅ TR (reflexive property);
• ∠QTR ≅ ∠STR (given);
• QT ≅ ST (given).

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

• QR ≅ SR
• ∠QRT ≅ ∠SRT

Angles QRT and SRT are supplementary (add up to 180°). Since these two angles are congruent, they have the same measure equal to $\frac{1}{2}\cdot 180^{\circ}=90^{\circ}$

So, true options are

m∠QRT = 90°

m∠QRT = m∠SRT

Answer 2

Answer: ∠S ≅ ∠U

Step-by-step explanation: I just took the test and got the answer right