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
2 answers:
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
So, true options are
m∠QRT = 90°
m∠QRT = m∠SRT
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Hope this helped and I’ve shown my work and the answer! :)
