contestada

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

Respuesta :

frika

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 [tex]\frac{1}{2}\cdot 180^{\circ}=90^{\circ}[/tex]

So, true options are

m∠QRT = 90°

m∠QRT = m∠SRT

Ver imagen frika

Answer:

The correct options are;

m[tex]\angle[/tex]QRT [tex]=90^o[/tex]

m[tex]\angle[/tex]QRT [tex]=[/tex] m[tex]\angle[/tex]SRT

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. [tex]\angle[/tex]QTR ≅ [tex]\angle[/tex]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. [tex]\angle[/tex]QRT ≅ [tex]\angle[/tex]SRT

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

That will be

[tex]=(180/2)\\=90 ^o[/tex]

Hence, The correct options are;

m[tex]\angle[/tex]QRT [tex]=90^o[/tex]

m[tex]\angle[/tex]QRT [tex]=[/tex] m[tex]\angle[/tex]SRT

For more information visit;

https://brainly.com/question/22062407?referrer=searchResults

ACCESS MORE