Question

In the diagram below, QRS is an equilateral triangle and RT QS.


Which statement must be true?

A. QRT is a 30-60-90 triangle.
B. RT = 2 • QT
C. QR = RT
D. QRT is a 45-45-90 triangle.

Answer 1

Because the triangle is an equilateral triangle, this means that all angles are 60 degrees, and all sides are the same length. The question states that line RT bisects line QS at a perpendicular angle.

Line RT bisects angle R as a result. When a line bisects an angle, the angle is divided by 2. Find the new angle of R:

$60 \div 2 = 30$

The new angle of R is 30 for both triangles.

The square denotes a right angle, which is 90 degrees. We'll focus on triangle QRT, as it is the triangle listed in most answers.

Two of its angles have measures of 30 degrees and 90 degrees. A triangle's internal angles must all add up to 180. To find the missing angle, set up the following equation where the missing angle = x:

$x + 30 + 90 = 180$
$x + 120 = 180$

Subtract 120 from both sides to get x by itself:

$x = 60$

The three angles of triangle QRT are 30, 60, and 90, making it a 30-60-90 triangle.

The answer is A. QRT is a 30-60-90 triangle.

Answer 2

Answer:

Option A is correct QRT is a 30-60-90 triangle.

Step-by-step explanation:

Given QRS is an equilateral triangle                                                ∴ ∠QRS=∠RSQ=∠SQR=60°

and also RT is perpendicular to QS implies ∠RTQ = 90°

In triangle QRT, by angle sum property of triangle

∠RQT+∠QTR+∠QRT=180°

⇒ 60°+90°+∠QRT=180°

⇒ ∠QRT=180°-60°-90°=30°

Hence, we can say that option A is correct QRT is a 30-60-90 triangle.